Optimal. Leaf size=27 \[ -\frac{1}{2 b (1-3 m) \left (a+b x^{1-3 m}\right )^2} \]
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Rubi [A] time = 0.0137646, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {1593, 261} \[ -\frac{1}{2 b (1-3 m) \left (a+b x^{1-3 m}\right )^2} \]
Antiderivative was successfully verified.
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Rule 1593
Rule 261
Rubi steps
\begin{align*} \int \frac{1}{\left (b x^{1-2 m}+a x^m\right )^3} \, dx &=\int \frac{x^{-3 m}}{\left (a+b x^{1-3 m}\right )^3} \, dx\\ &=-\frac{1}{2 b (1-3 m) \left (a+b x^{1-3 m}\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0185168, size = 27, normalized size = 1. \[ -\frac{1}{2 b (1-3 m) \left (a+b x^{1-3 m}\right )^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.02, size = 39, normalized size = 1.4 \begin{align*} -{\frac{ \left ( 2\,a \left ({x}^{m} \right ) ^{3}+bx \right ) x}{ \left ( -2+6\,m \right ){a}^{2} \left ( a \left ({x}^{m} \right ) ^{3}+bx \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.10417, size = 89, normalized size = 3.3 \begin{align*} -\frac{2 \, a x x^{3 \, m} + b x^{2}}{2 \,{\left (2 \, a^{3} b{\left (3 \, m - 1\right )} x x^{3 \, m} + a^{2} b^{2}{\left (3 \, m - 1\right )} x^{2} + a^{4}{\left (3 \, m - 1\right )} x^{6 \, m}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 0.893229, size = 162, normalized size = 6. \begin{align*} -\frac{2 \, a x x^{3 \, m} + b x^{2}}{2 \,{\left (2 \,{\left (3 \, a^{3} b m - a^{3} b\right )} x x^{3 \, m} +{\left (3 \, a^{2} b^{2} m - a^{2} b^{2}\right )} x^{2} +{\left (3 \, a^{4} m - a^{4}\right )} x^{6 \, m}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (a x^{m} + b x^{-2 \, m + 1}\right )}^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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