Optimal. Leaf size=28 \[ -\frac {x^3}{3 b}-\frac {a \log \left (a-b x^3\right )}{3 b^2} \]
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Rubi [A]
time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {272, 45}
\begin {gather*} -\frac {a \log \left (a-b x^3\right )}{3 b^2}-\frac {x^3}{3 b} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int \frac {x^5}{a-b x^3} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {x}{a-b x} \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (-\frac {1}{b}-\frac {a}{b (-a+b x)}\right ) \, dx,x,x^3\right )\\ &=-\frac {x^3}{3 b}-\frac {a \log \left (a-b x^3\right )}{3 b^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 28, normalized size = 1.00 \begin {gather*} -\frac {x^3}{3 b}-\frac {a \log \left (a-b x^3\right )}{3 b^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 25, normalized size = 0.89
method | result | size |
default | \(-\frac {x^{3}}{3 b}-\frac {a \ln \left (-b \,x^{3}+a \right )}{3 b^{2}}\) | \(25\) |
norman | \(-\frac {x^{3}}{3 b}-\frac {a \ln \left (-b \,x^{3}+a \right )}{3 b^{2}}\) | \(25\) |
risch | \(-\frac {x^{3}}{3 b}-\frac {a \ln \left (-b \,x^{3}+a \right )}{3 b^{2}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 25, normalized size = 0.89 \begin {gather*} -\frac {x^{3}}{3 \, b} - \frac {a \log \left (b x^{3} - a\right )}{3 \, b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 23, normalized size = 0.82 \begin {gather*} -\frac {b x^{3} + a \log \left (b x^{3} - a\right )}{3 \, b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 22, normalized size = 0.79 \begin {gather*} - \frac {a \log {\left (- a + b x^{3} \right )}}{3 b^{2}} - \frac {x^{3}}{3 b} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.64, size = 26, normalized size = 0.93 \begin {gather*} -\frac {x^{3}}{3 \, b} - \frac {a \log \left ({\left | b x^{3} - a \right |}\right )}{3 \, b^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 23, normalized size = 0.82 \begin {gather*} -\frac {b\,x^3+a\,\ln \left (b\,x^3-a\right )}{3\,b^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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