Optimal. Leaf size=65 \[ \frac{10}{9} a^2 b^3 x^9+\frac{5}{3} a^3 b^2 x^6+\frac{5}{3} a^4 b x^3+a^5 \log (x)+\frac{5}{12} a b^4 x^{12}+\frac{b^5 x^{15}}{15} \]
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Rubi [A] time = 0.0333262, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{10}{9} a^2 b^3 x^9+\frac{5}{3} a^3 b^2 x^6+\frac{5}{3} a^4 b x^3+a^5 \log (x)+\frac{5}{12} a b^4 x^{12}+\frac{b^5 x^{15}}{15} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b x^3\right )^5}{x} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^5}{x} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (5 a^4 b+\frac{a^5}{x}+10 a^3 b^2 x+10 a^2 b^3 x^2+5 a b^4 x^3+b^5 x^4\right ) \, dx,x,x^3\right )\\ &=\frac{5}{3} a^4 b x^3+\frac{5}{3} a^3 b^2 x^6+\frac{10}{9} a^2 b^3 x^9+\frac{5}{12} a b^4 x^{12}+\frac{b^5 x^{15}}{15}+a^5 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0042221, size = 65, normalized size = 1. \[ \frac{10}{9} a^2 b^3 x^9+\frac{5}{3} a^3 b^2 x^6+\frac{5}{3} a^4 b x^3+a^5 \log (x)+\frac{5}{12} a b^4 x^{12}+\frac{b^5 x^{15}}{15} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 56, normalized size = 0.9 \begin{align*}{\frac{5\,{a}^{4}b{x}^{3}}{3}}+{\frac{5\,{a}^{3}{b}^{2}{x}^{6}}{3}}+{\frac{10\,{a}^{2}{b}^{3}{x}^{9}}{9}}+{\frac{5\,a{b}^{4}{x}^{12}}{12}}+{\frac{{b}^{5}{x}^{15}}{15}}+{a}^{5}\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.973242, size = 78, normalized size = 1.2 \begin{align*} \frac{1}{15} \, b^{5} x^{15} + \frac{5}{12} \, a b^{4} x^{12} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{5}{3} \, a^{3} b^{2} x^{6} + \frac{5}{3} \, a^{4} b x^{3} + \frac{1}{3} \, a^{5} \log \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67939, size = 134, normalized size = 2.06 \begin{align*} \frac{1}{15} \, b^{5} x^{15} + \frac{5}{12} \, a b^{4} x^{12} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{5}{3} \, a^{3} b^{2} x^{6} + \frac{5}{3} \, a^{4} b x^{3} + a^{5} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.32187, size = 65, normalized size = 1. \begin{align*} a^{5} \log{\left (x \right )} + \frac{5 a^{4} b x^{3}}{3} + \frac{5 a^{3} b^{2} x^{6}}{3} + \frac{10 a^{2} b^{3} x^{9}}{9} + \frac{5 a b^{4} x^{12}}{12} + \frac{b^{5} x^{15}}{15} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12789, size = 76, normalized size = 1.17 \begin{align*} \frac{1}{15} \, b^{5} x^{15} + \frac{5}{12} \, a b^{4} x^{12} + \frac{10}{9} \, a^{2} b^{3} x^{9} + \frac{5}{3} \, a^{3} b^{2} x^{6} + \frac{5}{3} \, a^{4} b x^{3} + a^{5} \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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