Optimal. Leaf size=18 \[ \text {Int}\left (x^m f^{\frac {c}{(a+b x)^2}},x\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int f^{\frac {c}{(a+b x)^2}} x^m \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int f^{\frac {c}{(a+b x)^2}} x^m \, dx &=\int f^{\frac {c}{(a+b x)^2}} x^m \, dx\\ \end {align*}
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Mathematica [A] time = 0.09, size = 0, normalized size = 0.00 \[ \int f^{\frac {c}{(a+b x)^2}} x^m \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (f^{\frac {c}{b^{2} x^{2} + 2 \, a b x + a^{2}}} x^{m}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int f^{\frac {c}{{\left (b x + a\right )}^{2}}} x^{m}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 0, normalized size = 0.00 \[ \int f^{\frac {c}{\left (b x +a \right )^{2}}} x^{m}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int f^{\frac {c}{{\left (b x + a\right )}^{2}}} x^{m}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.06 \[ \int f^{\frac {c}{{\left (a+b\,x\right )}^2}}\,x^m \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int f^{\frac {c}{\left (a + b x\right )^{2}}} x^{m}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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