Optimal. Leaf size=514 \[ \frac{3 a b^2 \sinh ^{-1}(a+b x) \text{PolyLog}\left (2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )}{\left (a^2+1\right )^{3/2}}-\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{PolyLog}\left (2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )}{\left (a^2+1\right )^{3/2}}+\frac{3 b^2 \text{PolyLog}\left (2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )}{a^2+1}+\frac{3 b^2 \text{PolyLog}\left (2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )}{a^2+1}-\frac{3 a b^2 \text{PolyLog}\left (3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )}{\left (a^2+1\right )^{3/2}}+\frac{3 a b^2 \text{PolyLog}\left (3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )}{\left (a^2+1\right )^{3/2}}-\frac{3 b^2 \sinh ^{-1}(a+b x)^2}{2 \left (a^2+1\right )}+\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )}{2 \left (a^2+1\right )^{3/2}}-\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )}{2 \left (a^2+1\right )^{3/2}}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )}{a^2+1}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )}{a^2+1}-\frac{3 b \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{2 \left (a^2+1\right ) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2} \]
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Rubi [A] time = 0.883413, antiderivative size = 514, normalized size of antiderivative = 1., number of steps used = 21, number of rules used = 13, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 1.083, Rules used = {5865, 5801, 5831, 3324, 3322, 2264, 2190, 2531, 2282, 6589, 5561, 2279, 2391} \[ \frac{3 a b^2 \sinh ^{-1}(a+b x) \text{PolyLog}\left (2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )}{\left (a^2+1\right )^{3/2}}-\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{PolyLog}\left (2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )}{\left (a^2+1\right )^{3/2}}+\frac{3 b^2 \text{PolyLog}\left (2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )}{a^2+1}+\frac{3 b^2 \text{PolyLog}\left (2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )}{a^2+1}-\frac{3 a b^2 \text{PolyLog}\left (3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )}{\left (a^2+1\right )^{3/2}}+\frac{3 a b^2 \text{PolyLog}\left (3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )}{\left (a^2+1\right )^{3/2}}-\frac{3 b^2 \sinh ^{-1}(a+b x)^2}{2 \left (a^2+1\right )}+\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )}{2 \left (a^2+1\right )^{3/2}}-\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )}{2 \left (a^2+1\right )^{3/2}}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )}{a^2+1}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )}{a^2+1}-\frac{3 b \sqrt{(a+b x)^2+1} \sinh ^{-1}(a+b x)^2}{2 \left (a^2+1\right ) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2} \]
Antiderivative was successfully verified.
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Rule 5865
Rule 5801
Rule 5831
Rule 3324
Rule 3322
Rule 2264
Rule 2190
Rule 2531
Rule 2282
Rule 6589
Rule 5561
Rule 2279
Rule 2391
Rubi steps
\begin{align*} \int \frac{\sinh ^{-1}(a+b x)^3}{x^3} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{\sinh ^{-1}(x)^3}{\left (-\frac{a}{b}+\frac{x}{b}\right )^3} \, dx,x,a+b x\right )}{b}\\ &=-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}+\frac{3}{2} \operatorname{Subst}\left (\int \frac{\sinh ^{-1}(x)^2}{\left (-\frac{a}{b}+\frac{x}{b}\right )^2 \sqrt{1+x^2}} \, dx,x,a+b x\right )\\ &=-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}+\frac{3}{2} \operatorname{Subst}\left (\int \frac{x^2}{\left (-\frac{a}{b}+\frac{\sinh (x)}{b}\right )^2} \, dx,x,\sinh ^{-1}(a+b x)\right )\\ &=-\frac{3 b \sqrt{1+(a+b x)^2} \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right ) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}+\frac{(3 b) \operatorname{Subst}\left (\int \frac{x \cosh (x)}{-\frac{a}{b}+\frac{\sinh (x)}{b}} \, dx,x,\sinh ^{-1}(a+b x)\right )}{1+a^2}-\frac{(3 a b) \operatorname{Subst}\left (\int \frac{x^2}{-\frac{a}{b}+\frac{\sinh (x)}{b}} \, dx,x,\sinh ^{-1}(a+b x)\right )}{2 \left (1+a^2\right )}\\ &=-\frac{3 b^2 \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right )}-\frac{3 b \sqrt{1+(a+b x)^2} \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right ) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}+\frac{(3 b) \operatorname{Subst}\left (\int \frac{e^x x}{-\frac{a}{b}-\frac{\sqrt{1+a^2}}{b}+\frac{e^x}{b}} \, dx,x,\sinh ^{-1}(a+b x)\right )}{1+a^2}+\frac{(3 b) \operatorname{Subst}\left (\int \frac{e^x x}{-\frac{a}{b}+\frac{\sqrt{1+a^2}}{b}+\frac{e^x}{b}} \, dx,x,\sinh ^{-1}(a+b x)\right )}{1+a^2}-\frac{(3 a b) \operatorname{Subst}\left (\int \frac{e^x x^2}{-\frac{1}{b}-\frac{2 a e^x}{b}+\frac{e^{2 x}}{b}} \, dx,x,\sinh ^{-1}(a+b x)\right )}{1+a^2}\\ &=-\frac{3 b^2 \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right )}-\frac{3 b \sqrt{1+(a+b x)^2} \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right ) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{1+a^2}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{1+a^2}-\frac{(3 a b) \operatorname{Subst}\left (\int \frac{e^x x^2}{-\frac{2 a}{b}-\frac{2 \sqrt{1+a^2}}{b}+\frac{2 e^x}{b}} \, dx,x,\sinh ^{-1}(a+b x)\right )}{\left (1+a^2\right )^{3/2}}+\frac{(3 a b) \operatorname{Subst}\left (\int \frac{e^x x^2}{-\frac{2 a}{b}+\frac{2 \sqrt{1+a^2}}{b}+\frac{2 e^x}{b}} \, dx,x,\sinh ^{-1}(a+b x)\right )}{\left (1+a^2\right )^{3/2}}-\frac{\left (3 b^2\right ) \operatorname{Subst}\left (\int \log \left (1+\frac{e^x}{\left (-\frac{a}{b}-\frac{\sqrt{1+a^2}}{b}\right ) b}\right ) \, dx,x,\sinh ^{-1}(a+b x)\right )}{1+a^2}-\frac{\left (3 b^2\right ) \operatorname{Subst}\left (\int \log \left (1+\frac{e^x}{\left (-\frac{a}{b}+\frac{\sqrt{1+a^2}}{b}\right ) b}\right ) \, dx,x,\sinh ^{-1}(a+b x)\right )}{1+a^2}\\ &=-\frac{3 b^2 \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right )}-\frac{3 b \sqrt{1+(a+b x)^2} \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right ) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{1+a^2}+\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{2 \left (1+a^2\right )^{3/2}}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{1+a^2}-\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{2 \left (1+a^2\right )^{3/2}}+\frac{\left (3 a b^2\right ) \operatorname{Subst}\left (\int x \log \left (1+\frac{2 e^x}{\left (-\frac{2 a}{b}-\frac{2 \sqrt{1+a^2}}{b}\right ) b}\right ) \, dx,x,\sinh ^{-1}(a+b x)\right )}{\left (1+a^2\right )^{3/2}}-\frac{\left (3 a b^2\right ) \operatorname{Subst}\left (\int x \log \left (1+\frac{2 e^x}{\left (-\frac{2 a}{b}+\frac{2 \sqrt{1+a^2}}{b}\right ) b}\right ) \, dx,x,\sinh ^{-1}(a+b x)\right )}{\left (1+a^2\right )^{3/2}}-\frac{\left (3 b^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{x}{\left (-\frac{a}{b}-\frac{\sqrt{1+a^2}}{b}\right ) b}\right )}{x} \, dx,x,e^{\sinh ^{-1}(a+b x)}\right )}{1+a^2}-\frac{\left (3 b^2\right ) \operatorname{Subst}\left (\int \frac{\log \left (1+\frac{x}{\left (-\frac{a}{b}+\frac{\sqrt{1+a^2}}{b}\right ) b}\right )}{x} \, dx,x,e^{\sinh ^{-1}(a+b x)}\right )}{1+a^2}\\ &=-\frac{3 b^2 \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right )}-\frac{3 b \sqrt{1+(a+b x)^2} \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right ) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{1+a^2}+\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{2 \left (1+a^2\right )^{3/2}}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{1+a^2}-\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{2 \left (1+a^2\right )^{3/2}}+\frac{3 b^2 \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{1+a^2}+\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{\left (1+a^2\right )^{3/2}}+\frac{3 b^2 \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{1+a^2}-\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{\left (1+a^2\right )^{3/2}}+\frac{\left (3 a b^2\right ) \operatorname{Subst}\left (\int \text{Li}_2\left (-\frac{2 e^x}{\left (-\frac{2 a}{b}-\frac{2 \sqrt{1+a^2}}{b}\right ) b}\right ) \, dx,x,\sinh ^{-1}(a+b x)\right )}{\left (1+a^2\right )^{3/2}}-\frac{\left (3 a b^2\right ) \operatorname{Subst}\left (\int \text{Li}_2\left (-\frac{2 e^x}{\left (-\frac{2 a}{b}+\frac{2 \sqrt{1+a^2}}{b}\right ) b}\right ) \, dx,x,\sinh ^{-1}(a+b x)\right )}{\left (1+a^2\right )^{3/2}}\\ &=-\frac{3 b^2 \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right )}-\frac{3 b \sqrt{1+(a+b x)^2} \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right ) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{1+a^2}+\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{2 \left (1+a^2\right )^{3/2}}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{1+a^2}-\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{2 \left (1+a^2\right )^{3/2}}+\frac{3 b^2 \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{1+a^2}+\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{\left (1+a^2\right )^{3/2}}+\frac{3 b^2 \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{1+a^2}-\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{\left (1+a^2\right )^{3/2}}-\frac{\left (3 a b^2\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (\frac{x}{a-\sqrt{1+a^2}}\right )}{x} \, dx,x,e^{\sinh ^{-1}(a+b x)}\right )}{\left (1+a^2\right )^{3/2}}+\frac{\left (3 a b^2\right ) \operatorname{Subst}\left (\int \frac{\text{Li}_2\left (\frac{x}{a+\sqrt{1+a^2}}\right )}{x} \, dx,x,e^{\sinh ^{-1}(a+b x)}\right )}{\left (1+a^2\right )^{3/2}}\\ &=-\frac{3 b^2 \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right )}-\frac{3 b \sqrt{1+(a+b x)^2} \sinh ^{-1}(a+b x)^2}{2 \left (1+a^2\right ) x}-\frac{\sinh ^{-1}(a+b x)^3}{2 x^2}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{1+a^2}+\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{2 \left (1+a^2\right )^{3/2}}+\frac{3 b^2 \sinh ^{-1}(a+b x) \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{1+a^2}-\frac{3 a b^2 \sinh ^{-1}(a+b x)^2 \log \left (1-\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{2 \left (1+a^2\right )^{3/2}}+\frac{3 b^2 \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{1+a^2}+\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{\left (1+a^2\right )^{3/2}}+\frac{3 b^2 \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{1+a^2}-\frac{3 a b^2 \sinh ^{-1}(a+b x) \text{Li}_2\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{\left (1+a^2\right )^{3/2}}-\frac{3 a b^2 \text{Li}_3\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{1+a^2}}\right )}{\left (1+a^2\right )^{3/2}}+\frac{3 a b^2 \text{Li}_3\left (\frac{e^{\sinh ^{-1}(a+b x)}}{a+\sqrt{1+a^2}}\right )}{\left (1+a^2\right )^{3/2}}\\ \end{align*}
Mathematica [A] time = 0.235749, size = 524, normalized size = 1.02 \[ \frac{6 b^2 x^2 \left (\sqrt{a^2+1}+a \sinh ^{-1}(a+b x)\right ) \text{PolyLog}\left (2,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )+6 b^2 x^2 \left (\sqrt{a^2+1}-a \sinh ^{-1}(a+b x)\right ) \text{PolyLog}\left (2,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )-6 a b^2 x^2 \text{PolyLog}\left (3,\frac{e^{\sinh ^{-1}(a+b x)}}{a-\sqrt{a^2+1}}\right )+6 a b^2 x^2 \text{PolyLog}\left (3,\frac{e^{\sinh ^{-1}(a+b x)}}{\sqrt{a^2+1}+a}\right )-3 \sqrt{a^2+1} b^2 x^2 \sinh ^{-1}(a+b x)^2-3 \sqrt{a^2+1} b x \sqrt{a^2+2 a b x+b^2 x^2+1} \sinh ^{-1}(a+b x)^2-3 a b^2 x^2 \sinh ^{-1}(a+b x)^2 \log \left (\frac{\sqrt{a^2+1}-e^{\sinh ^{-1}(a+b x)}+a}{\sqrt{a^2+1}+a}\right )+3 a b^2 x^2 \sinh ^{-1}(a+b x)^2 \log \left (\frac{\sqrt{a^2+1}+e^{\sinh ^{-1}(a+b x)}-a}{\sqrt{a^2+1}-a}\right )+6 \sqrt{a^2+1} b^2 x^2 \sinh ^{-1}(a+b x) \log \left (\frac{\sqrt{a^2+1}-e^{\sinh ^{-1}(a+b x)}+a}{\sqrt{a^2+1}+a}\right )+6 \sqrt{a^2+1} b^2 x^2 \sinh ^{-1}(a+b x) \log \left (\frac{\sqrt{a^2+1}+e^{\sinh ^{-1}(a+b x)}-a}{\sqrt{a^2+1}-a}\right )-a^2 \sqrt{a^2+1} \sinh ^{-1}(a+b x)^3-\sqrt{a^2+1} \sinh ^{-1}(a+b x)^3}{2 \left (a^2+1\right )^{3/2} x^2} \]
Antiderivative was successfully verified.
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Maple [F] time = 0.299, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\it Arcsinh} \left ( bx+a \right ) \right ) ^{3}}{{x}^{3}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \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 (\frac{\operatorname{arsinh}\left (b x + a\right )^{3}}{x^{3}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{asinh}^{3}{\left (a + b x \right )}}{x^{3}}\, dx \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 \frac{\operatorname{arsinh}\left (b x + a\right )^{3}}{x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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