Optimal. Leaf size=16 \[ \frac{x^5}{3 \sqrt{c x^4}} \]
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Rubi [A] time = 0.0015658, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13, Rules used = {1, 15, 30} \[ \frac{x^5}{3 \sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Rule 1
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{x^4}{\sqrt{2+2 a-2 (1+a)+c x^4}} \, dx &=\int \frac{x^4}{\sqrt{c x^4}} \, dx\\ &=\frac{x^2 \int x^2 \, dx}{\sqrt{c x^4}}\\ &=\frac{x^5}{3 \sqrt{c x^4}}\\ \end{align*}
Mathematica [A] time = 0.002233, size = 16, normalized size = 1. \[ \frac{x^5}{3 \sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.044, size = 13, normalized size = 0.8 \begin{align*}{\frac{{x}^{5}}{3}{\frac{1}{\sqrt{c{x}^{4}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.955182, size = 16, normalized size = 1. \begin{align*} \frac{x^{5}}{3 \, \sqrt{c x^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.26011, size = 28, normalized size = 1.75 \begin{align*} \frac{\sqrt{c x^{4}} x}{3 \, c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.532797, size = 15, normalized size = 0.94 \begin{align*} \frac{x^{5}}{3 \sqrt{c} \sqrt{x^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21064, size = 11, normalized size = 0.69 \begin{align*} \frac{x^{3}}{3 \, \sqrt{c}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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