Optimal. Leaf size=15 \[ \frac {\log \left (a+c x^4\right )}{4 c} \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {260} \[ \frac {\log \left (a+c x^4\right )}{4 c} \]
Antiderivative was successfully verified.
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Rule 260
Rubi steps
\begin {align*} \int \frac {x^3}{a+c x^4} \, dx &=\frac {\log \left (a+c x^4\right )}{4 c}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ \frac {\log \left (a+c x^4\right )}{4 c} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 13, normalized size = 0.87 \[ \frac {\log \left (c x^{4} + a\right )}{4 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 14, normalized size = 0.93 \[ \frac {\log \left ({\left | c x^{4} + a \right |}\right )}{4 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.93 \[ \frac {\ln \left (c \,x^{4}+a \right )}{4 c} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 13, normalized size = 0.87 \[ \frac {\log \left (c x^{4} + a\right )}{4 \, c} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.87 \[ \frac {\ln \left (c\,x^4+a\right )}{4\,c} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 10, normalized size = 0.67 \[ \frac {\log {\left (a + c x^{4} \right )}}{4 c} \]
Verification of antiderivative is not currently implemented for this CAS.
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