Optimal. Leaf size=16 \[ \frac{x^4}{2 \sqrt{c x^4}} \]
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Rubi [A] time = 0.0017394, 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} \[ \frac{x^4}{2 \sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Rule 1
Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{x^3}{\sqrt{2+2 a-2 (1+a)+c x^4}} \, dx &=\int \frac{x^3}{\sqrt{c x^4}} \, dx\\ &=\frac{x^2 \int x \, dx}{\sqrt{c x^4}}\\ &=\frac{x^4}{2 \sqrt{c x^4}}\\ \end{align*}
Mathematica [A] time = 0.0016441, size = 16, normalized size = 1. \[ \frac{x^4}{2 \sqrt{c x^4}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.042, size = 13, normalized size = 0.8 \begin{align*}{\frac{{x}^{4}}{2}{\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 = 0.946274, size = 16, normalized size = 1. \begin{align*} \frac{\sqrt{c x^{4}}}{2 \, c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.22158, size = 26, normalized size = 1.62 \begin{align*} \frac{\sqrt{c x^{4}}}{2 \, c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.465126, size = 15, normalized size = 0.94 \begin{align*} \frac{x^{4}}{2 \sqrt{c} \sqrt{x^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.25238, size = 11, normalized size = 0.69 \begin{align*} \frac{x^{2}}{2 \, \sqrt{c}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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