Optimal. Leaf size=18 \[ \text{Int}\left (x^m f^{\frac{c}{(a+b x)^2}},x\right ) \]
[Out]
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Rubi [A] time = 0.0645127, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (f^{\frac{c}{(a+b x)^2}} x^m,x\right ) \]
Verification is Not applicable to the result.
[In] Int[f^(c/(a + b*x)^2)*x^m,x]
[Out]
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Rubi in Sympy [A] time = 0., size = 0, normalized size = 0. \[ \int f^{\frac{c}{\left (a + b x\right )^{2}}} x^{m}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(c/(b*x+a)**2)*x**m,x)
[Out]
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Mathematica [A] time = 0.0748207, size = 0, normalized size = 0. \[ \int f^{\frac{c}{(a+b x)^2}} x^m \, dx \]
Verification is Not applicable to the result.
[In] Integrate[f^(c/(a + b*x)^2)*x^m,x]
[Out]
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Maple [A] time = 0.064, size = 0, normalized size = 0. \[ \int{f}^{{\frac{c}{ \left ( bx+a \right ) ^{2}}}}{x}^{m}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(c/(b*x+a)^2)*x^m,x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int f^{\frac{c}{{\left (b x + a\right )}^{2}}} x^{m}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(c/(b*x + a)^2)*x^m,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (f^{\frac{c}{b^{2} x^{2} + 2 \, a b x + a^{2}}} x^{m}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(c/(b*x + a)^2)*x^m,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(c/(b*x+a)**2)*x**m,x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int f^{\frac{c}{{\left (b x + a\right )}^{2}}} x^{m}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(c/(b*x + a)^2)*x^m,x, algorithm="giac")
[Out]