Optimal. Leaf size=2050 \[ \text{result too large to display} \]
[Out]
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Rubi [A] time = 6.89069, antiderivative size = 2050, normalized size of antiderivative = 1., number of steps used = 148, number of rules used = 32, integrand size = 32, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 1., Rules used = {2439, 2416, 2389, 2296, 2295, 2401, 2390, 2305, 2304, 2396, 2433, 2374, 2383, 6589, 6742, 2411, 2346, 2302, 30, 2330, 2430, 2301, 43, 2394, 2393, 2391, 2375, 2317, 2334, 12, 14, 2395} \[ \text{result too large to display} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2439
Rule 2416
Rule 2389
Rule 2296
Rule 2295
Rule 2401
Rule 2390
Rule 2305
Rule 2304
Rule 2396
Rule 2433
Rule 2374
Rule 2383
Rule 6589
Rule 6742
Rule 2411
Rule 2346
Rule 2302
Rule 30
Rule 2330
Rule 2430
Rule 2301
Rule 43
Rule 2394
Rule 2393
Rule 2391
Rule 2375
Rule 2317
Rule 2334
Rule 12
Rule 14
Rule 2395
Rubi steps
\begin{align*} \int x \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right ) \, dx &=\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{1}{2} (g j m) \int \frac{x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{397+j x} \, dx-\frac{1}{2} (3 b e n) \int \frac{x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \left (f+g \log \left (h (397+j x)^m\right )\right )}{d+e x} \, dx\\ &=\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{1}{2} (g j m) \int \left (-\frac{397 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{j^2}+\frac{x \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{j}+\frac{157609 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{j^2 (397+j x)}\right ) \, dx-\frac{1}{2} (3 b e n) \int \left (\frac{f x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{d+e x}+\frac{g x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{d+e x}\right ) \, dx\\ &=\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{1}{2} (g m) \int x \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \, dx+\frac{(397 g m) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \, dx}{2 j}-\frac{(157609 g m) \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^3}{397+j x} \, dx}{2 j}-\frac{1}{2} (3 b e f n) \int \frac{x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{d+e x} \, dx-\frac{1}{2} (3 b e g n) \int \frac{x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{d+e x} \, dx\\ &=-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{1}{2} (g m) \int \left (-\frac{d \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{e}+\frac{(d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{e}\right ) \, dx+\frac{(397 g m) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^3 \, dx,x,d+e x\right )}{2 e j}-\frac{1}{2} (3 b f n) \operatorname{Subst}\left (\int \frac{\left (-\frac{d}{e}+\frac{x}{e}\right )^2 \left (a+b \log \left (c x^n\right )\right )^2}{x} \, dx,x,d+e x\right )-\frac{1}{2} (3 b e g n) \int \left (-\frac{d \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{e^2}+\frac{x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{e}+\frac{d^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{e^2 (d+e x)}\right ) \, dx+\frac{(472827 b e g m n) \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{2 j^2}\\ &=\frac{397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{(g m) \int (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \, dx}{2 e}+\frac{(d g m) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \, dx}{2 e}-\frac{(3 b f n) \operatorname{Subst}\left (\int \left (-\frac{d}{e}+\frac{x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e}+\frac{(3 b d f n) \operatorname{Subst}\left (\int \frac{\left (-\frac{d}{e}+\frac{x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )^2}{x} \, dx,x,d+e x\right )}{2 e}-\frac{1}{2} (3 b g n) \int x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right ) \, dx+\frac{(3 b d g n) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right ) \, dx}{2 e}-\frac{\left (3 b d^2 g n\right ) \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{d+e x} \, dx}{2 e}+\frac{(472827 b g m n) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right )^2 \log \left (\frac{e \left (\frac{397 e-d j}{e}+\frac{j x}{e}\right )}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 j^2}-\frac{(1191 b g m n) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e j}\\ &=-\frac{1191 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e j}+\frac{397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}+\frac{3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac{3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac{(g m) \operatorname{Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right )^3 \, dx,x,d+e x\right )}{2 e^2}+\frac{(d g m) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^3 \, dx,x,d+e x\right )}{2 e^2}+\frac{(3 b d f n) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e^2}-\frac{\left (3 b d^2 f n\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right )^2}{x} \, dx,x,d+e x\right )}{2 e^2}-\frac{(3 b f n) \operatorname{Subst}\left (\int \left (-\frac{d \left (a+b \log \left (c x^n\right )\right )^2}{e}+\frac{x \left (a+b \log \left (c x^n\right )\right )^2}{e}\right ) \, dx,x,d+e x\right )}{2 e}-\frac{\left (3 b d^2 g n\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right )^2 \log \left (h \left (\frac{397 e-d j}{e}+\frac{j x}{e}\right )^m\right )}{x} \, dx,x,d+e x\right )}{2 e^2}+\frac{1}{4} (3 b g j m n) \int \frac{x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{397+j x} \, dx-\frac{(3 b d g j m n) \int \frac{x \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{397+j x} \, dx}{2 e}-\left (3 b^2 d g n^2\right ) \int \frac{x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{d+e x} \, dx+\frac{1}{2} \left (3 b^2 e g n^2\right ) \int \frac{x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{d+e x} \, dx+\frac{\left (472827 b^2 g m n^2\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right ) \text{Li}_2\left (-\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{j^2}+\frac{\left (1191 b^2 g m n^2\right ) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{e j}\\ &=\frac{1191 a b^2 g m n^2 x}{j}+\frac{3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e^2}-\frac{1191 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e j}+\frac{d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac{g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}+\frac{3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac{3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac{d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}-\frac{\left (3 d^2 f\right ) \operatorname{Subst}\left (\int x^2 \, dx,x,a+b \log \left (c (d+e x)^n\right )\right )}{2 e^2}+\frac{\left (d^2 g j m\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right )^3}{\frac{397 e-d j}{e}+\frac{j x}{e}} \, dx,x,d+e x\right )}{2 e^3}-\frac{(3 b f n) \operatorname{Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e^2}+\frac{(3 b d f n) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e^2}+\frac{(3 b g m n) \operatorname{Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{4 e^2}-\frac{(3 b d g m n) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e^2}+\frac{1}{4} (3 b g j m n) \int \left (-\frac{397 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j^2}+\frac{x \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j}+\frac{157609 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j^2 (397+j x)}\right ) \, dx-\frac{(3 b d g j m n) \int \left (\frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j}-\frac{397 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j (397+j x)}\right ) \, dx}{2 e}-\frac{\left (3 b^2 d f n^2\right ) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{e^2}-\left (3 b^2 d g n^2\right ) \int \left (\frac{\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{e}-\frac{d \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{e (d+e x)}\right ) \, dx+\frac{1}{2} \left (3 b^2 e g n^2\right ) \int \left (-\frac{d \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{e^2}+\frac{x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{e}+\frac{d^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{e^2 (d+e x)}\right ) \, dx+\frac{\left (1191 b^3 g m n^2\right ) \operatorname{Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e j}-\frac{\left (472827 b^3 g m n^3\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_3\left (-\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{j^2}\\ &=-\frac{3 a b^2 d f n^2 x}{e}+\frac{1191 a b^2 g m n^2 x}{j}-\frac{1191 b^3 g m n^3 x}{j}+\frac{1191 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e j}+\frac{3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac{3 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e^2}-\frac{1191 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e j}-\frac{3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac{3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{8 e^2}-\frac{d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac{g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}+\frac{3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac{3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac{d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )+\frac{d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}-\frac{472827 b^3 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}+\frac{1}{4} (3 b g m n) \int x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx-\frac{\left (3 b d^2 g m n\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 e^2}-\frac{(3 b d g m n) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx}{2 e}+\frac{(1191 b d g m n) \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^2}{397+j x} \, dx}{2 e}-\frac{(1191 b g m n) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx}{4 j}+\frac{(472827 b g m n) \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right )^2}{397+j x} \, dx}{4 j}+\frac{\left (3 b^2 f n^2\right ) \operatorname{Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{2 e^2}-\frac{\left (3 b^2 d f n^2\right ) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{e^2}-\frac{\left (3 b^3 d f n^2\right ) \operatorname{Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e^2}+\frac{1}{2} \left (3 b^2 g n^2\right ) \int x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right ) \, dx-\frac{\left (3 b^2 d g n^2\right ) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right ) \, dx}{2 e}-\frac{\left (3 b^2 d g n^2\right ) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right ) \, dx}{e}+\frac{\left (3 b^2 d^2 g n^2\right ) \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{d+e x} \, dx}{2 e}+\frac{\left (3 b^2 d^2 g n^2\right ) \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{d+e x} \, dx}{e}-\frac{\left (3 b^2 g m n^2\right ) \operatorname{Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{4 e^2}+\frac{\left (3 b^2 d g m n^2\right ) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{e^2}\\ &=-\frac{6 a b^2 d f n^2 x}{e}+\frac{3 a b^2 d g m n^2 x}{e}+\frac{1191 a b^2 g m n^2 x}{j}+\frac{3 b^3 d f n^3 x}{e}-\frac{1191 b^3 g m n^3 x}{j}-\frac{3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac{3 b^3 g m n^3 (d+e x)^2}{16 e^2}-\frac{3 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{1191 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e j}+\frac{3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac{3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{8 e^2}+\frac{3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac{3 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e^2}-\frac{1191 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e j}-\frac{3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac{3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{8 e^2}-\frac{d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac{g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}+\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac{1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac{9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac{3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac{3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac{3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac{d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )+\frac{d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac{3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}-\frac{472827 b^3 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}+\frac{1}{4} (3 b g m n) \int \left (-\frac{d \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e}+\frac{(d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e}\right ) \, dx-\frac{(3 b d g m n) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e^2}-\frac{(1191 b g m n) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{4 e j}-\frac{\left (3 b^3 d f n^2\right ) \operatorname{Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e^2}+\frac{\left (3 b^2 d^2 g n^2\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right ) \log \left (h \left (\frac{397 e-d j}{e}+\frac{j x}{e}\right )^m\right )}{x} \, dx,x,d+e x\right )}{2 e^2}+\frac{\left (3 b^2 d^2 g n^2\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right ) \log \left (h \left (\frac{397 e-d j}{e}+\frac{j x}{e}\right )^m\right )}{x} \, dx,x,d+e x\right )}{e^2}+\frac{\left (3 b^3 d g m n^2\right ) \operatorname{Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e^2}-\frac{\left (3 b^2 d^2 g m n^2\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right ) \text{Li}_2\left (-\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e^2}-\frac{\left (472827 b^2 e g m n^2\right ) \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{2 j^2}-\frac{\left (1191 b^2 d g m n^2\right ) \int \frac{\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{j}-\frac{1}{4} \left (3 b^2 g j m n^2\right ) \int \frac{x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{397+j x} \, dx+\frac{\left (3 b^2 d g j m n^2\right ) \int \frac{x \left (a+b \log \left (c (d+e x)^n\right )\right )}{397+j x} \, dx}{2 e}+\frac{\left (3 b^2 d g j m n^2\right ) \int \frac{x \left (a+b \log \left (c (d+e x)^n\right )\right )}{397+j x} \, dx}{e}+\frac{1}{2} \left (3 b^3 d g n^3\right ) \int \frac{x \log \left (h (397+j x)^m\right )}{d+e x} \, dx+\left (3 b^3 d g n^3\right ) \int \frac{x \log \left (h (397+j x)^m\right )}{d+e x} \, dx-\frac{1}{4} \left (3 b^3 e g n^3\right ) \int \frac{x^2 \log \left (h (397+j x)^m\right )}{d+e x} \, dx\\ &=-\frac{6 a b^2 d f n^2 x}{e}+\frac{3 a b^2 d g m n^2 x}{e}+\frac{1191 a b^2 g m n^2 x}{j}+\frac{6 b^3 d f n^3 x}{e}-\frac{3 b^3 d g m n^3 x}{e}-\frac{1191 b^3 g m n^3 x}{j}-\frac{3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac{3 b^3 g m n^3 (d+e x)^2}{16 e^2}-\frac{6 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{3 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{1191 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e j}+\frac{3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac{3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{8 e^2}+\frac{3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac{3 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac{3573 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e j}-\frac{3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac{3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{8 e^2}-\frac{d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac{g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}+\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac{1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac{9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac{3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac{9 b d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{4 e^2}+\frac{3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac{3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac{d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )+\frac{d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac{3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac{3 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}-\frac{472827 b^3 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}+\frac{(3 b g m n) \int (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx}{4 e}-\frac{(3 b d g m n) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx}{4 e}-\frac{\left (3 b d^2 g j m n\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right )^2}{\frac{397 e-d j}{e}+\frac{j x}{e}} \, dx,x,d+e x\right )}{4 e^3}-\frac{\left (3 b d^2 g j m n\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right )^2}{\frac{397 e-d j}{e}+\frac{j x}{e}} \, dx,x,d+e x\right )}{2 e^3}+\frac{\left (3 b^2 d g m n^2\right ) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{e^2}-\frac{\left (472827 b^2 g m n^2\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right ) \log \left (\frac{e \left (\frac{397 e-d j}{e}+\frac{j x}{e}\right )}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 j^2}+\frac{\left (1191 b^2 g m n^2\right ) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{2 e j}-\frac{\left (1191 b^2 d g m n^2\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right ) \log \left (\frac{e \left (\frac{397 e-d j}{e}+\frac{j x}{e}\right )}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e j}-\frac{1}{4} \left (3 b^2 g j m n^2\right ) \int \left (-\frac{397 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j^2}+\frac{x \left (a+b \log \left (c (d+e x)^n\right )\right )}{j}+\frac{157609 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j^2 (397+j x)}\right ) \, dx+\frac{\left (3 b^2 d g j m n^2\right ) \int \left (\frac{a+b \log \left (c (d+e x)^n\right )}{j}-\frac{397 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j (397+j x)}\right ) \, dx}{2 e}+\frac{\left (3 b^2 d g j m n^2\right ) \int \left (\frac{a+b \log \left (c (d+e x)^n\right )}{j}-\frac{397 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j (397+j x)}\right ) \, dx}{e}+\frac{1}{2} \left (3 b^3 d g n^3\right ) \int \left (\frac{\log \left (h (397+j x)^m\right )}{e}-\frac{d \log \left (h (397+j x)^m\right )}{e (d+e x)}\right ) \, dx+\left (3 b^3 d g n^3\right ) \int \left (\frac{\log \left (h (397+j x)^m\right )}{e}-\frac{d \log \left (h (397+j x)^m\right )}{e (d+e x)}\right ) \, dx-\frac{1}{4} \left (3 b^3 e g n^3\right ) \int \left (-\frac{d \log \left (h (397+j x)^m\right )}{e^2}+\frac{x \log \left (h (397+j x)^m\right )}{e}+\frac{d^2 \log \left (h (397+j x)^m\right )}{e^2 (d+e x)}\right ) \, dx+\frac{\left (3 b^3 d^2 g m n^3\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_3\left (-\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e^2}\\ &=-\frac{6 a b^2 d f n^2 x}{e}+\frac{6 a b^2 d g m n^2 x}{e}+\frac{3573 a b^2 g m n^2 x}{2 j}+\frac{6 b^3 d f n^3 x}{e}-\frac{3 b^3 d g m n^3 x}{e}-\frac{1191 b^3 g m n^3 x}{j}-\frac{3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac{3 b^3 g m n^3 (d+e x)^2}{16 e^2}-\frac{6 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{3 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{1191 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e j}+\frac{3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac{3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{8 e^2}+\frac{3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac{3 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac{3573 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e j}-\frac{3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac{3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{8 e^2}-\frac{d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac{g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}+\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac{1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac{9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac{3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac{9 b d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{4 e^2}+\frac{3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac{3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac{d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{9 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{4 e^2}+\frac{d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac{1191 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e j}+\frac{3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac{3 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}+\frac{3 b^3 d^2 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e^2}-\frac{472827 b^3 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}+\frac{(3 b g m n) \operatorname{Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{4 e^2}-\frac{(3 b d g m n) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{4 e^2}-\frac{1}{4} \left (3 b^2 g m n^2\right ) \int x \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx+\frac{\left (3 b^3 d g m n^2\right ) \operatorname{Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e^2}+\frac{\left (3 b^2 d^2 g m n^2\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right ) \log \left (1+\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 e^2}+\frac{\left (3 b^2 d^2 g m n^2\right ) \operatorname{Subst}\left (\int \frac{\left (a+b \log \left (c x^n\right )\right ) \log \left (1+\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e^2}+\frac{\left (3 b^2 d g m n^2\right ) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx}{2 e}+\frac{\left (3 b^2 d g m n^2\right ) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx}{e}-\frac{\left (1191 b^2 d g m n^2\right ) \int \frac{a+b \log \left (c (d+e x)^n\right )}{397+j x} \, dx}{2 e}-\frac{\left (1191 b^2 d g m n^2\right ) \int \frac{a+b \log \left (c (d+e x)^n\right )}{397+j x} \, dx}{e}+\frac{\left (1191 b^2 g m n^2\right ) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx}{4 j}-\frac{\left (472827 b^2 g m n^2\right ) \int \frac{a+b \log \left (c (d+e x)^n\right )}{397+j x} \, dx}{4 j}+\frac{\left (1191 b^3 g m n^2\right ) \operatorname{Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{2 e j}-\frac{1}{4} \left (3 b^3 g n^3\right ) \int x \log \left (h (397+j x)^m\right ) \, dx+\frac{\left (3 b^3 d g n^3\right ) \int \log \left (h (397+j x)^m\right ) \, dx}{4 e}+\frac{\left (3 b^3 d g n^3\right ) \int \log \left (h (397+j x)^m\right ) \, dx}{2 e}+\frac{\left (3 b^3 d g n^3\right ) \int \log \left (h (397+j x)^m\right ) \, dx}{e}-\frac{\left (3 b^3 d^2 g n^3\right ) \int \frac{\log \left (h (397+j x)^m\right )}{d+e x} \, dx}{4 e}-\frac{\left (3 b^3 d^2 g n^3\right ) \int \frac{\log \left (h (397+j x)^m\right )}{d+e x} \, dx}{2 e}-\frac{\left (3 b^3 d^2 g n^3\right ) \int \frac{\log \left (h (397+j x)^m\right )}{d+e x} \, dx}{e}-\frac{\left (472827 b^3 g m n^3\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 j^2}-\frac{\left (1191 b^3 d g m n^3\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e j}\\ &=-\frac{6 a b^2 d f n^2 x}{e}+\frac{21 a b^2 d g m n^2 x}{2 e}+\frac{8337 a b^2 g m n^2 x}{4 j}+\frac{6 b^3 d f n^3 x}{e}-\frac{6 b^3 d g m n^3 x}{e}-\frac{3573 b^3 g m n^3 x}{2 j}-\frac{3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac{3 b^3 g m n^3 (d+e x)^2}{16 e^2}-\frac{6 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{6 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{3573 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{2 e j}-\frac{3}{8} b^2 g m n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )+\frac{3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac{3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{8 e^2}+\frac{3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac{15 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac{3573 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e j}-\frac{3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac{3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac{d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac{g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}-\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{4 j^2}-\frac{3573 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 e j}+\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac{1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac{3}{8} b^3 g n^3 x^2 \log \left (h (397+j x)^m\right )-\frac{21 b^3 d^2 g n^3 \log \left (-\frac{j (d+e x)}{397 e-d j}\right ) \log \left (h (397+j x)^m\right )}{4 e^2}-\frac{9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac{3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac{9 b d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{4 e^2}+\frac{3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac{3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac{d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{9 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{4 e^2}+\frac{d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{9 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac{1191 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e j}+\frac{3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac{472827 b^3 g m n^3 \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac{1191 b^3 d g m n^3 \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e j}-\frac{3 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}+\frac{3 b^3 d^2 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e^2}-\frac{472827 b^3 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}-\frac{\left (3 b^2 g m n^2\right ) \operatorname{Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{4 e^2}+\frac{\left (3 b^2 d g m n^2\right ) \operatorname{Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{2 e^2}+\frac{\left (3 b^3 d g m n^2\right ) \int \log \left (c (d+e x)^n\right ) \, dx}{2 e}+\frac{\left (3 b^3 d g m n^2\right ) \int \log \left (c (d+e x)^n\right ) \, dx}{e}+\frac{\left (1191 b^3 g m n^2\right ) \int \log \left (c (d+e x)^n\right ) \, dx}{4 j}+\frac{\left (3 b^3 d g n^3\right ) \operatorname{Subst}\left (\int \log \left (h x^m\right ) \, dx,x,397+j x\right )}{4 e j}+\frac{\left (3 b^3 d g n^3\right ) \operatorname{Subst}\left (\int \log \left (h x^m\right ) \, dx,x,397+j x\right )}{2 e j}+\frac{\left (3 b^3 d g n^3\right ) \operatorname{Subst}\left (\int \log \left (h x^m\right ) \, dx,x,397+j x\right )}{e j}+\frac{\left (3 b^3 d^2 g m n^3\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 e^2}+\frac{\left (3 b^3 d^2 g m n^3\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (-\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e^2}+\frac{1}{8} \left (3 b^3 e g m n^3\right ) \int \frac{x^2}{d+e x} \, dx+\frac{\left (472827 b^3 e g m n^3\right ) \int \frac{\log \left (\frac{e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{4 j^2}+\frac{\left (1191 b^3 d g m n^3\right ) \int \frac{\log \left (\frac{e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{2 j}+\frac{\left (1191 b^3 d g m n^3\right ) \int \frac{\log \left (\frac{e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{j}+\frac{1}{8} \left (3 b^3 g j m n^3\right ) \int \frac{x^2}{397+j x} \, dx+\frac{\left (3 b^3 d^2 g j m n^3\right ) \int \frac{\log \left (\frac{j (d+e x)}{-397 e+d j}\right )}{397+j x} \, dx}{4 e^2}+\frac{\left (3 b^3 d^2 g j m n^3\right ) \int \frac{\log \left (\frac{j (d+e x)}{-397 e+d j}\right )}{397+j x} \, dx}{2 e^2}+\frac{\left (3 b^3 d^2 g j m n^3\right ) \int \frac{\log \left (\frac{j (d+e x)}{-397 e+d j}\right )}{397+j x} \, dx}{e^2}\\ &=-\frac{6 a b^2 d f n^2 x}{e}+\frac{12 a b^2 d g m n^2 x}{e}+\frac{8337 a b^2 g m n^2 x}{4 j}+\frac{6 b^3 d f n^3 x}{e}-\frac{45 b^3 d g m n^3 x}{4 e}-\frac{3573 b^3 g m n^3 x}{2 j}-\frac{3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac{3 b^3 g m n^3 (d+e x)^2}{8 e^2}-\frac{6 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{6 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{3573 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{2 e j}-\frac{3}{8} b^2 g m n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )+\frac{3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac{3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}+\frac{3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac{15 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac{3573 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e j}-\frac{3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac{3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac{d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac{g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}-\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{4 j^2}-\frac{3573 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 e j}+\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac{1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac{3}{8} b^3 g n^3 x^2 \log \left (h (397+j x)^m\right )+\frac{21 b^3 d g n^3 (397+j x) \log \left (h (397+j x)^m\right )}{4 e j}-\frac{21 b^3 d^2 g n^3 \log \left (-\frac{j (d+e x)}{397 e-d j}\right ) \log \left (h (397+j x)^m\right )}{4 e^2}-\frac{9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac{3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac{9 b d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{4 e^2}+\frac{3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac{3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac{d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{9 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{4 e^2}+\frac{d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{9 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac{1191 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e j}+\frac{3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac{9 b^3 d^2 g m n^3 \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{472827 b^3 g m n^3 \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac{1191 b^3 d g m n^3 \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e j}-\frac{3 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}+\frac{3 b^3 d^2 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e^2}-\frac{472827 b^3 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}+2 \frac{\left (3 b^3 d g m n^2\right ) \operatorname{Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{2 e^2}+\frac{\left (3 b^3 d g m n^2\right ) \operatorname{Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e^2}+\frac{\left (1191 b^3 g m n^2\right ) \operatorname{Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{4 e j}+\frac{\left (3 b^3 d^2 g m n^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{e x}{-397 e+d j}\right )}{x} \, dx,x,397+j x\right )}{4 e^2}+\frac{\left (3 b^3 d^2 g m n^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{e x}{-397 e+d j}\right )}{x} \, dx,x,397+j x\right )}{2 e^2}+\frac{\left (3 b^3 d^2 g m n^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{e x}{-397 e+d j}\right )}{x} \, dx,x,397+j x\right )}{e^2}+\frac{1}{8} \left (3 b^3 e g m n^3\right ) \int \left (-\frac{d}{e^2}+\frac{x}{e}+\frac{d^2}{e^2 (d+e x)}\right ) \, dx+\frac{\left (472827 b^3 g m n^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{4 j^2}+\frac{\left (1191 b^3 d g m n^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 e j}+\frac{\left (1191 b^3 d g m n^3\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e j}+\frac{1}{8} \left (3 b^3 g j m n^3\right ) \int \left (-\frac{397}{j^2}+\frac{x}{j}+\frac{157609}{j^2 (397+j x)}\right ) \, dx\\ &=-\frac{6 a b^2 d f n^2 x}{e}+\frac{12 a b^2 d g m n^2 x}{e}+\frac{8337 a b^2 g m n^2 x}{4 j}+\frac{6 b^3 d f n^3 x}{e}-\frac{117 b^3 d g m n^3 x}{8 e}-\frac{17865 b^3 g m n^3 x}{8 j}+\frac{3}{8} b^3 g m n^3 x^2-\frac{3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac{3 b^3 g m n^3 (d+e x)^2}{8 e^2}+\frac{3 b^3 d^2 g m n^3 \log (d+e x)}{8 e^2}-\frac{6 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{9 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac{8337 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{4 e j}-\frac{3}{8} b^2 g m n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )+\frac{3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac{3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}+\frac{3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac{15 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac{3573 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e j}-\frac{3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac{3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac{d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac{397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac{g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}+2 \left (-\frac{3 b^3 d g m n^3 x}{2 e}+\frac{3 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{2 e^2}\right )+\frac{472827 b^3 g m n^3 \log (397+j x)}{8 j^2}-\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{4 j^2}-\frac{3573 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 e j}+\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac{1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac{157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac{e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac{3}{8} b^3 g n^3 x^2 \log \left (h (397+j x)^m\right )+\frac{21 b^3 d g n^3 (397+j x) \log \left (h (397+j x)^m\right )}{4 e j}-\frac{21 b^3 d^2 g n^3 \log \left (-\frac{j (d+e x)}{397 e-d j}\right ) \log \left (h (397+j x)^m\right )}{4 e^2}-\frac{9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac{3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac{9 b d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{4 e^2}+\frac{3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac{3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac{d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac{1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac{9 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{4 e^2}+\frac{d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{472827 b^3 g m n^3 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{4 j^2}-\frac{3573 b^3 d g m n^3 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e j}-\frac{9 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac{1191 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e j}+\frac{3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text{Li}_2\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac{21 b^3 d^2 g m n^3 \text{Li}_2\left (\frac{e (397+j x)}{397 e-d j}\right )}{4 e^2}+\frac{9 b^3 d^2 g m n^3 \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac{472827 b^3 g m n^3 \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac{1191 b^3 d g m n^3 \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e j}-\frac{3 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e^2}+\frac{472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text{Li}_3\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}+\frac{3 b^3 d^2 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{e^2}-\frac{472827 b^3 g m n^3 \text{Li}_4\left (-\frac{j (d+e x)}{397 e-d j}\right )}{j^2}\\ \end{align*}
Mathematica [B] time = 3.38738, size = 4971, normalized size = 2.42 \[ \text{Result too large to show} \]
Antiderivative was successfully verified.
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Maple [F] time = 2.901, size = 0, normalized size = 0. \begin{align*} \int x \left ( a+b\ln \left ( c \left ( ex+d \right ) ^{n} \right ) \right ) ^{3} \left ( f+g\ln \left ( h \left ( jx+i \right ) ^{m} \right ) \right ) \, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (b^{3} f x \log \left ({\left (e x + d\right )}^{n} c\right )^{3} + 3 \, a b^{2} f x \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + 3 \, a^{2} b f x \log \left ({\left (e x + d\right )}^{n} c\right ) + a^{3} f x +{\left (b^{3} g x \log \left ({\left (e x + d\right )}^{n} c\right )^{3} + 3 \, a b^{2} g x \log \left ({\left (e x + d\right )}^{n} c\right )^{2} + 3 \, a^{2} b g x \log \left ({\left (e x + d\right )}^{n} c\right ) + a^{3} g x\right )} \log \left ({\left (j x + i\right )}^{m} h\right ), x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{3}{\left (g \log \left ({\left (j x + i\right )}^{m} h\right ) + f\right )} x\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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