3.244 \(\int f^{\frac{c}{(a+b x)^2}} x^m \, dx\)

Optimal. Leaf size=18 \[ \text{Int}\left (x^m f^{\frac{c}{(a+b x)^2}},x\right ) \]

[Out]

CannotIntegrate[f^(c/(a + b*x)^2)*x^m, x]

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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]

Defer[Int][f^(c/(a + b*x)^2)*x^m, x]

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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]

Integral(f**(c/(a + b*x)**2)*x**m, x)

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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]

Integrate[f^(c/(a + b*x)^2)*x^m, x]

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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]

int(f^(c/(b*x+a)^2)*x^m,x)

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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]

integrate(f^(c/(b*x + a)^2)*x^m, x)

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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]

integral(f^(c/(b^2*x^2 + 2*a*b*x + a^2))*x^m, x)

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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]

Timed 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]

integrate(f^(c/(b*x + a)^2)*x^m, x)