Optimal. Leaf size=28 \[ -\frac {3 \left (a+b x^2\right )^{7/3}}{14 a c (c x)^{14/3}} \]
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Rubi [A]
time = 0.00, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {270}
\begin {gather*} -\frac {3 \left (a+b x^2\right )^{7/3}}{14 a c (c x)^{14/3}} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^{4/3}}{(c x)^{17/3}} \, dx &=-\frac {3 \left (a+b x^2\right )^{7/3}}{14 a c (c x)^{14/3}}\\ \end {align*}
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Mathematica [A]
time = 1.97, size = 26, normalized size = 0.93 \begin {gather*} -\frac {3 x \left (a+b x^2\right )^{7/3}}{14 a (c x)^{17/3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 21, normalized size = 0.75
method | result | size |
gosper | \(-\frac {3 x \left (b \,x^{2}+a \right )^{\frac {7}{3}}}{14 a \left (c x \right )^{\frac {17}{3}}}\) | \(21\) |
risch | \(-\frac {3 \left (b \,x^{2}+a \right )^{\frac {1}{3}} \left (b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right )}{14 c^{5} \left (c x \right )^{\frac {2}{3}} x^{4} a}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.38, size = 43, normalized size = 1.54 \begin {gather*} -\frac {3 \, {\left (b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right )} {\left (b x^{2} + a\right )}^{\frac {1}{3}} \left (c x\right )^{\frac {1}{3}}}{14 \, a c^{6} x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \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 [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\left (b\,x^2+a\right )}^{4/3}}{{\left (c\,x\right )}^{17/3}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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