Optimal. Leaf size=25 \[ \frac{a^2 x^5}{5}+\frac{2}{3} a b x^3+b^2 x \]
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Rubi [A] time = 0.0089196, antiderivative size = 25, 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 = {263, 194} \[ \frac{a^2 x^5}{5}+\frac{2}{3} a b x^3+b^2 x \]
Antiderivative was successfully verified.
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Rule 263
Rule 194
Rubi steps
\begin{align*} \int \left (a+\frac{b}{x^2}\right )^2 x^4 \, dx &=\int \left (b+a x^2\right )^2 \, dx\\ &=\int \left (b^2+2 a b x^2+a^2 x^4\right ) \, dx\\ &=b^2 x+\frac{2}{3} a b x^3+\frac{a^2 x^5}{5}\\ \end{align*}
Mathematica [A] time = 0.0010089, size = 25, normalized size = 1. \[ \frac{a^2 x^5}{5}+\frac{2}{3} a b x^3+b^2 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 22, normalized size = 0.9 \begin{align*}{b}^{2}x+{\frac{2\,{x}^{3}ab}{3}}+{\frac{{x}^{5}{a}^{2}}{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.961557, size = 28, normalized size = 1.12 \begin{align*} \frac{1}{5} \, a^{2} x^{5} + \frac{2}{3} \, a b x^{3} + b^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38841, size = 47, normalized size = 1.88 \begin{align*} \frac{1}{5} \, a^{2} x^{5} + \frac{2}{3} \, a b x^{3} + b^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.059351, size = 22, normalized size = 0.88 \begin{align*} \frac{a^{2} x^{5}}{5} + \frac{2 a b x^{3}}{3} + b^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17198, size = 28, normalized size = 1.12 \begin{align*} \frac{1}{5} \, a^{2} x^{5} + \frac{2}{3} \, a b x^{3} + b^{2} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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