Optimal. Leaf size=46 \[ a c \log (x)+a d x+\frac{1}{2} a e x^2+\frac{1}{3} b c x^3+\frac{1}{4} b d x^4+\frac{1}{5} b e x^5 \]
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Rubi [A] time = 0.0245177, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {1628} \[ a c \log (x)+a d x+\frac{1}{2} a e x^2+\frac{1}{3} b c x^3+\frac{1}{4} b d x^4+\frac{1}{5} b e x^5 \]
Antiderivative was successfully verified.
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Rule 1628
Rubi steps
\begin{align*} \int \frac{\left (c+d x+e x^2\right ) \left (a+b x^3\right )}{x} \, dx &=\int \left (a d+\frac{a c}{x}+a e x+b c x^2+b d x^3+b e x^4\right ) \, dx\\ &=a d x+\frac{1}{2} a e x^2+\frac{1}{3} b c x^3+\frac{1}{4} b d x^4+\frac{1}{5} b e x^5+a c \log (x)\\ \end{align*}
Mathematica [A] time = 0.0041212, size = 46, normalized size = 1. \[ a c \log (x)+a d x+\frac{1}{2} a e x^2+\frac{1}{3} b c x^3+\frac{1}{4} b d x^4+\frac{1}{5} b e x^5 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 39, normalized size = 0.9 \begin{align*} adx+{\frac{ae{x}^{2}}{2}}+{\frac{bc{x}^{3}}{3}}+{\frac{bd{x}^{4}}{4}}+{\frac{be{x}^{5}}{5}}+ac\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.949336, size = 51, normalized size = 1.11 \begin{align*} \frac{1}{5} \, b e x^{5} + \frac{1}{4} \, b d x^{4} + \frac{1}{3} \, b c x^{3} + \frac{1}{2} \, a e x^{2} + a d x + a c \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49063, size = 103, normalized size = 2.24 \begin{align*} \frac{1}{5} \, b e x^{5} + \frac{1}{4} \, b d x^{4} + \frac{1}{3} \, b c x^{3} + \frac{1}{2} \, a e x^{2} + a d x + a c \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.272387, size = 44, normalized size = 0.96 \begin{align*} a c \log{\left (x \right )} + a d x + \frac{a e x^{2}}{2} + \frac{b c x^{3}}{3} + \frac{b d x^{4}}{4} + \frac{b e x^{5}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08311, size = 55, normalized size = 1.2 \begin{align*} \frac{1}{5} \, b x^{5} e + \frac{1}{4} \, b d x^{4} + \frac{1}{3} \, b c x^{3} + \frac{1}{2} \, a x^{2} e + a d x + a c \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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