Optimal. Leaf size=27 \[ \frac{x^4}{4 c}-\frac{a \log \left (a+c x^4\right )}{4 c^2} \]
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Rubi [A] time = 0.019002, antiderivative size = 27, 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} \[ \frac{x^4}{4 c}-\frac{a \log \left (a+c x^4\right )}{4 c^2} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^7}{a+c x^4} \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int \frac{x}{a+c x} \, dx,x,x^4\right )\\ &=\frac{1}{4} \operatorname{Subst}\left (\int \left (\frac{1}{c}-\frac{a}{c (a+c x)}\right ) \, dx,x,x^4\right )\\ &=\frac{x^4}{4 c}-\frac{a \log \left (a+c x^4\right )}{4 c^2}\\ \end{align*}
Mathematica [A] time = 0.0055033, size = 27, normalized size = 1. \[ \frac{x^4}{4 c}-\frac{a \log \left (a+c x^4\right )}{4 c^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 24, normalized size = 0.9 \begin{align*}{\frac{{x}^{4}}{4\,c}}-{\frac{a\ln \left ( c{x}^{4}+a \right ) }{4\,{c}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.96025, size = 31, normalized size = 1.15 \begin{align*} \frac{x^{4}}{4 \, c} - \frac{a \log \left (c x^{4} + a\right )}{4 \, c^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45827, size = 49, normalized size = 1.81 \begin{align*} \frac{c x^{4} - a \log \left (c x^{4} + a\right )}{4 \, c^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.331674, size = 20, normalized size = 0.74 \begin{align*} - \frac{a \log{\left (a + c x^{4} \right )}}{4 c^{2}} + \frac{x^{4}}{4 c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.62132, size = 32, normalized size = 1.19 \begin{align*} \frac{x^{4}}{4 \, c} - \frac{a \log \left ({\left | c x^{4} + a \right |}\right )}{4 \, c^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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