Optimal. Leaf size=552 \[ \frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left (\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left (\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left (\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{12 b^{7/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left (\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left (\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left (\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{12 b^{7/2} d}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}-\frac{40 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}+\frac{32 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{5 b d \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}} \]
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Rubi [A] time = 1.77558, antiderivative size = 552, normalized size of antiderivative = 1., number of steps used = 34, number of rules used = 9, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.36, Rules used = {5866, 12, 5668, 5775, 5666, 3307, 2180, 2204, 2205} \[ \frac{\sqrt{\pi } e^4 e^{a/b} \text{Erf}\left (\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{Erf}\left (\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{Erf}\left (\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{12 b^{7/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{Erfi}\left (\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{Erfi}\left (\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{Erfi}\left (\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{12 b^{7/2} d}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}-\frac{40 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}+\frac{32 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{5 b d \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}} \]
Antiderivative was successfully verified.
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Rule 5866
Rule 12
Rule 5668
Rule 5775
Rule 5666
Rule 3307
Rule 2180
Rule 2204
Rule 2205
Rubi steps
\begin{align*} \int \frac{(c e+d e x)^4}{\left (a+b \cosh ^{-1}(c+d x)\right )^{7/2}} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{e^4 x^4}{\left (a+b \cosh ^{-1}(x)\right )^{7/2}} \, dx,x,c+d x\right )}{d}\\ &=\frac{e^4 \operatorname{Subst}\left (\int \frac{x^4}{\left (a+b \cosh ^{-1}(x)\right )^{7/2}} \, dx,x,c+d x\right )}{d}\\ &=-\frac{2 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{5 b d \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}-\frac{\left (8 e^4\right ) \operatorname{Subst}\left (\int \frac{x^3}{\sqrt{-1+x} \sqrt{1+x} \left (a+b \cosh ^{-1}(x)\right )^{5/2}} \, dx,x,c+d x\right )}{5 b d}+\frac{\left (2 e^4\right ) \operatorname{Subst}\left (\int \frac{x^5}{\sqrt{-1+x} \sqrt{1+x} \left (a+b \cosh ^{-1}(x)\right )^{5/2}} \, dx,x,c+d x\right )}{b d}\\ &=-\frac{2 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{5 b d \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}-\frac{\left (16 e^4\right ) \operatorname{Subst}\left (\int \frac{x^2}{\left (a+b \cosh ^{-1}(x)\right )^{3/2}} \, dx,x,c+d x\right )}{5 b^2 d}+\frac{\left (20 e^4\right ) \operatorname{Subst}\left (\int \frac{x^4}{\left (a+b \cosh ^{-1}(x)\right )^{3/2}} \, dx,x,c+d x\right )}{3 b^2 d}\\ &=-\frac{2 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{5 b d \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}+\frac{32 e^4 \sqrt{-1+c+d x} (c+d x)^2 \sqrt{1+c+d x}}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{40 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{3 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{\left (32 e^4\right ) \operatorname{Subst}\left (\int \left (-\frac{\cosh (x)}{4 \sqrt{a+b x}}-\frac{3 \cosh (3 x)}{4 \sqrt{a+b x}}\right ) \, dx,x,\cosh ^{-1}(c+d x)\right )}{5 b^3 d}-\frac{\left (40 e^4\right ) \operatorname{Subst}\left (\int \left (-\frac{\cosh (x)}{8 \sqrt{a+b x}}-\frac{9 \cosh (3 x)}{16 \sqrt{a+b x}}-\frac{5 \cosh (5 x)}{16 \sqrt{a+b x}}\right ) \, dx,x,\cosh ^{-1}(c+d x)\right )}{3 b^3 d}\\ &=-\frac{2 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{5 b d \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}+\frac{32 e^4 \sqrt{-1+c+d x} (c+d x)^2 \sqrt{1+c+d x}}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{40 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{3 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{\left (8 e^4\right ) \operatorname{Subst}\left (\int \frac{\cosh (x)}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{5 b^3 d}+\frac{\left (5 e^4\right ) \operatorname{Subst}\left (\int \frac{\cosh (x)}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{3 b^3 d}+\frac{\left (25 e^4\right ) \operatorname{Subst}\left (\int \frac{\cosh (5 x)}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{6 b^3 d}-\frac{\left (24 e^4\right ) \operatorname{Subst}\left (\int \frac{\cosh (3 x)}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{5 b^3 d}+\frac{\left (15 e^4\right ) \operatorname{Subst}\left (\int \frac{\cosh (3 x)}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{2 b^3 d}\\ &=-\frac{2 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{5 b d \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}+\frac{32 e^4 \sqrt{-1+c+d x} (c+d x)^2 \sqrt{1+c+d x}}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{40 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{3 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{\left (4 e^4\right ) \operatorname{Subst}\left (\int \frac{e^{-x}}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{5 b^3 d}-\frac{\left (4 e^4\right ) \operatorname{Subst}\left (\int \frac{e^x}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{5 b^3 d}+\frac{\left (5 e^4\right ) \operatorname{Subst}\left (\int \frac{e^{-x}}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{6 b^3 d}+\frac{\left (5 e^4\right ) \operatorname{Subst}\left (\int \frac{e^x}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{6 b^3 d}+\frac{\left (25 e^4\right ) \operatorname{Subst}\left (\int \frac{e^{-5 x}}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{12 b^3 d}+\frac{\left (25 e^4\right ) \operatorname{Subst}\left (\int \frac{e^{5 x}}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{12 b^3 d}-\frac{\left (12 e^4\right ) \operatorname{Subst}\left (\int \frac{e^{-3 x}}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{5 b^3 d}-\frac{\left (12 e^4\right ) \operatorname{Subst}\left (\int \frac{e^{3 x}}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{5 b^3 d}+\frac{\left (15 e^4\right ) \operatorname{Subst}\left (\int \frac{e^{-3 x}}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{4 b^3 d}+\frac{\left (15 e^4\right ) \operatorname{Subst}\left (\int \frac{e^{3 x}}{\sqrt{a+b x}} \, dx,x,\cosh ^{-1}(c+d x)\right )}{4 b^3 d}\\ &=-\frac{2 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{5 b d \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}+\frac{32 e^4 \sqrt{-1+c+d x} (c+d x)^2 \sqrt{1+c+d x}}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{40 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{3 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{\left (8 e^4\right ) \operatorname{Subst}\left (\int e^{\frac{a}{b}-\frac{x^2}{b}} \, dx,x,\sqrt{a+b \cosh ^{-1}(c+d x)}\right )}{5 b^4 d}-\frac{\left (8 e^4\right ) \operatorname{Subst}\left (\int e^{-\frac{a}{b}+\frac{x^2}{b}} \, dx,x,\sqrt{a+b \cosh ^{-1}(c+d x)}\right )}{5 b^4 d}+\frac{\left (5 e^4\right ) \operatorname{Subst}\left (\int e^{\frac{a}{b}-\frac{x^2}{b}} \, dx,x,\sqrt{a+b \cosh ^{-1}(c+d x)}\right )}{3 b^4 d}+\frac{\left (5 e^4\right ) \operatorname{Subst}\left (\int e^{-\frac{a}{b}+\frac{x^2}{b}} \, dx,x,\sqrt{a+b \cosh ^{-1}(c+d x)}\right )}{3 b^4 d}+\frac{\left (25 e^4\right ) \operatorname{Subst}\left (\int e^{\frac{5 a}{b}-\frac{5 x^2}{b}} \, dx,x,\sqrt{a+b \cosh ^{-1}(c+d x)}\right )}{6 b^4 d}+\frac{\left (25 e^4\right ) \operatorname{Subst}\left (\int e^{-\frac{5 a}{b}+\frac{5 x^2}{b}} \, dx,x,\sqrt{a+b \cosh ^{-1}(c+d x)}\right )}{6 b^4 d}-\frac{\left (24 e^4\right ) \operatorname{Subst}\left (\int e^{\frac{3 a}{b}-\frac{3 x^2}{b}} \, dx,x,\sqrt{a+b \cosh ^{-1}(c+d x)}\right )}{5 b^4 d}-\frac{\left (24 e^4\right ) \operatorname{Subst}\left (\int e^{-\frac{3 a}{b}+\frac{3 x^2}{b}} \, dx,x,\sqrt{a+b \cosh ^{-1}(c+d x)}\right )}{5 b^4 d}+\frac{\left (15 e^4\right ) \operatorname{Subst}\left (\int e^{\frac{3 a}{b}-\frac{3 x^2}{b}} \, dx,x,\sqrt{a+b \cosh ^{-1}(c+d x)}\right )}{2 b^4 d}+\frac{\left (15 e^4\right ) \operatorname{Subst}\left (\int e^{-\frac{3 a}{b}+\frac{3 x^2}{b}} \, dx,x,\sqrt{a+b \cosh ^{-1}(c+d x)}\right )}{2 b^4 d}\\ &=-\frac{2 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{5 b d \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left (a+b \cosh ^{-1}(c+d x)\right )^{3/2}}+\frac{32 e^4 \sqrt{-1+c+d x} (c+d x)^2 \sqrt{1+c+d x}}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{40 e^4 \sqrt{-1+c+d x} (c+d x)^4 \sqrt{1+c+d x}}{3 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{e^4 e^{a/b} \sqrt{\pi } \text{erf}\left (\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{30 b^{7/2} d}+\frac{9 e^4 e^{\frac{3 a}{b}} \sqrt{3 \pi } \text{erf}\left (\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{20 b^{7/2} d}+\frac{5 e^4 e^{\frac{5 a}{b}} \sqrt{5 \pi } \text{erf}\left (\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{12 b^{7/2} d}+\frac{e^4 e^{-\frac{a}{b}} \sqrt{\pi } \text{erfi}\left (\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{30 b^{7/2} d}+\frac{9 e^4 e^{-\frac{3 a}{b}} \sqrt{3 \pi } \text{erfi}\left (\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{20 b^{7/2} d}+\frac{5 e^4 e^{-\frac{5 a}{b}} \sqrt{5 \pi } \text{erfi}\left (\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right )}{12 b^{7/2} d}\\ \end{align*}
Mathematica [A] time = 4.65917, size = 654, normalized size = 1.18 \[ \frac{e^4 \left (-4 \left (e^{-\cosh ^{-1}(c+d x)} \left (a+b \cosh ^{-1}(c+d x)\right ) \left (2 e^{\frac{a}{b}+\cosh ^{-1}(c+d x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left (a+b \cosh ^{-1}(c+d x)\right ) \text{Gamma}\left (\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right )-2 a-2 b \cosh ^{-1}(c+d x)+b\right )+e^{-\frac{a}{b}} \left (a+b \cosh ^{-1}(c+d x)\right ) \left (2 b \left (-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right )^{3/2} \text{Gamma}\left (\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right )+e^{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left (2 a+2 b \cosh ^{-1}(c+d x)+b\right )\right )+3 b^2 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1)\right )-9 \left (a+b \cosh ^{-1}(c+d x)\right ) \left (12 \sqrt{3} b e^{-\frac{3 a}{b}} \left (-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right )^{3/2} \text{Gamma}\left (\frac{1}{2},-\frac{3 \left (a+b \cosh ^{-1}(c+d x)\right )}{b}\right )+2 e^{-3 \cosh ^{-1}(c+d x)} \left (6 \sqrt{3} e^{3 \left (\frac{a}{b}+\cosh ^{-1}(c+d x)\right )} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left (a+b \cosh ^{-1}(c+d x)\right ) \text{Gamma}\left (\frac{1}{2},\frac{3 \left (a+b \cosh ^{-1}(c+d x)\right )}{b}\right )+6 a \left (e^{6 \cosh ^{-1}(c+d x)}-1\right )-6 b \cosh ^{-1}(c+d x)+b e^{6 \cosh ^{-1}(c+d x)} \left (6 \cosh ^{-1}(c+d x)+1\right )+b\right )\right )-5 \left (a+b \cosh ^{-1}(c+d x)\right ) \left (20 \sqrt{5} b e^{-\frac{5 a}{b}} \left (-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right )^{3/2} \text{Gamma}\left (\frac{1}{2},-\frac{5 \left (a+b \cosh ^{-1}(c+d x)\right )}{b}\right )+20 \sqrt{5} e^{\frac{5 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left (a+b \cosh ^{-1}(c+d x)\right ) \text{Gamma}\left (\frac{1}{2},\frac{5 \left (a+b \cosh ^{-1}(c+d x)\right )}{b}\right )+2 e^{-5 \cosh ^{-1}(c+d x)} \left (10 a \left (e^{10 \cosh ^{-1}(c+d x)}-1\right )-10 b \cosh ^{-1}(c+d x)+b e^{10 \cosh ^{-1}(c+d x)} \left (10 \cosh ^{-1}(c+d x)+1\right )+b\right )\right )-18 b^2 \sinh \left (3 \cosh ^{-1}(c+d x)\right )-6 b^2 \sinh \left (5 \cosh ^{-1}(c+d x)\right )\right )}{240 b^3 d \left (a+b \cosh ^{-1}(c+d x)\right )^{5/2}} \]
Warning: Unable to verify antiderivative.
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Maple [F] time = 0.329, size = 0, normalized size = 0. \begin{align*} \int{ \left ( dex+ce \right ) ^{4} \left ( a+b{\rm arccosh} \left (dx+c\right ) \right ) ^{-{\frac{7}{2}}}}\, 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*} \int \frac{{\left (d e x + c e\right )}^{4}}{{\left (b \operatorname{arcosh}\left (d x + c\right ) + a\right )}^{\frac{7}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \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*} \mathit{sage}_{0} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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