Optimal. Leaf size=21 \[ -\frac {\left (a+b x^3\right )^{2/3}}{2 a x^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {270}
\begin {gather*} -\frac {\left (a+b x^3\right )^{2/3}}{2 a x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {1}{x^3 \sqrt [3]{a+b x^3}} \, dx &=-\frac {\left (a+b x^3\right )^{2/3}}{2 a x^2}\\ \end {align*}
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Mathematica [A]
time = 0.09, size = 21, normalized size = 1.00 \begin {gather*} -\frac {\left (a+b x^3\right )^{2/3}}{2 a x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 18, normalized size = 0.86
method | result | size |
gosper | \(-\frac {\left (b \,x^{3}+a \right )^{\frac {2}{3}}}{2 a \,x^{2}}\) | \(18\) |
trager | \(-\frac {\left (b \,x^{3}+a \right )^{\frac {2}{3}}}{2 a \,x^{2}}\) | \(18\) |
risch | \(-\frac {\left (b \,x^{3}+a \right )^{\frac {2}{3}}}{2 a \,x^{2}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 17, normalized size = 0.81 \begin {gather*} -\frac {{\left (b x^{3} + a\right )}^{\frac {2}{3}}}{2 \, a x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 17, normalized size = 0.81 \begin {gather*} -\frac {{\left (b x^{3} + a\right )}^{\frac {2}{3}}}{2 \, a x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.33, size = 31, normalized size = 1.48 \begin {gather*} \frac {b^{\frac {2}{3}} \left (\frac {a}{b x^{3}} + 1\right )^{\frac {2}{3}} \Gamma \left (- \frac {2}{3}\right )}{3 a \Gamma \left (\frac {1}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.03, size = 17, normalized size = 0.81 \begin {gather*} -\frac {{\left (b\,x^3+a\right )}^{2/3}}{2\,a\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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