Optimal. Leaf size=66 \[ \frac{5}{3} a^2 b^3 x^6+\frac{10}{3} a^3 b^2 x^3+5 a^4 b \log (x)-\frac{a^5}{3 x^3}+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{12}}{12} \]
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Rubi [A] time = 0.0363388, antiderivative size = 66, 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} \[ \frac{5}{3} a^2 b^3 x^6+\frac{10}{3} a^3 b^2 x^3+5 a^4 b \log (x)-\frac{a^5}{3 x^3}+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{12}}{12} \]
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^4} \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \frac{(a+b x)^5}{x^2} \, dx,x,x^3\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (10 a^3 b^2+\frac{a^5}{x^2}+\frac{5 a^4 b}{x}+10 a^2 b^3 x+5 a b^4 x^2+b^5 x^3\right ) \, dx,x,x^3\right )\\ &=-\frac{a^5}{3 x^3}+\frac{10}{3} a^3 b^2 x^3+\frac{5}{3} a^2 b^3 x^6+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{12}}{12}+5 a^4 b \log (x)\\ \end{align*}
Mathematica [A] time = 0.0046972, size = 66, normalized size = 1. \[ \frac{5}{3} a^2 b^3 x^6+\frac{10}{3} a^3 b^2 x^3+5 a^4 b \log (x)-\frac{a^5}{3 x^3}+\frac{5}{9} a b^4 x^9+\frac{b^5 x^{12}}{12} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 57, normalized size = 0.9 \begin{align*} -{\frac{{a}^{5}}{3\,{x}^{3}}}+{\frac{10\,{a}^{3}{b}^{2}{x}^{3}}{3}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{6}}{3}}+{\frac{5\,a{b}^{4}{x}^{9}}{9}}+{\frac{{b}^{5}{x}^{12}}{12}}+5\,{a}^{4}b\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.981415, size = 78, normalized size = 1.18 \begin{align*} \frac{1}{12} \, b^{5} x^{12} + \frac{5}{9} \, a b^{4} x^{9} + \frac{5}{3} \, a^{2} b^{3} x^{6} + \frac{10}{3} \, a^{3} b^{2} x^{3} + \frac{5}{3} \, a^{4} b \log \left (x^{3}\right ) - \frac{a^{5}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72968, size = 143, normalized size = 2.17 \begin{align*} \frac{3 \, b^{5} x^{15} + 20 \, a b^{4} x^{12} + 60 \, a^{2} b^{3} x^{9} + 120 \, a^{3} b^{2} x^{6} + 180 \, a^{4} b x^{3} \log \left (x\right ) - 12 \, a^{5}}{36 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.391699, size = 65, normalized size = 0.98 \begin{align*} - \frac{a^{5}}{3 x^{3}} + 5 a^{4} b \log{\left (x \right )} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{6}}{3} + \frac{5 a b^{4} x^{9}}{9} + \frac{b^{5} x^{12}}{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10896, size = 90, normalized size = 1.36 \begin{align*} \frac{1}{12} \, b^{5} x^{12} + \frac{5}{9} \, a b^{4} x^{9} + \frac{5}{3} \, a^{2} b^{3} x^{6} + \frac{10}{3} \, a^{3} b^{2} x^{3} + 5 \, a^{4} b \log \left ({\left | x \right |}\right ) - \frac{5 \, a^{4} b x^{3} + a^{5}}{3 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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