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

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

[Out]

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

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Rubi [A]  time = 0.0677062, 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. \[ \text{Int}\left (\frac{f^{\frac{c}{(a+b x)^2}}}{x^2},x\right ) \]

Verification is Not applicable to the result.

[In]  Int[f^(c/(a + b*x)^2)/x^2,x]

[Out]

Defer[Int][f^(c/(a + b*x)^2)/x^2, x]

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Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{\left (a + b x\right )^{2}}}}{x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(f**(c/(b*x+a)**2)/x**2,x)

[Out]

Integral(f**(c/(a + b*x)**2)/x**2, x)

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Mathematica [A]  time = 0.173998, size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{(a+b x)^2}}}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]  Integrate[f^(c/(a + b*x)^2)/x^2,x]

[Out]

Integrate[f^(c/(a + b*x)^2)/x^2, x]

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Maple [A]  time = 0.043, size = 0, normalized size = 0. \[ \int{\frac{1}{{x}^{2}}{f}^{{\frac{c}{ \left ( bx+a \right ) ^{2}}}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(f^(c/(b*x+a)^2)/x^2,x)

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{{\left (b x + a\right )}^{2}}}}{x^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f^(c/(b*x + a)^2)/x^2,x, algorithm="maxima")

[Out]

integrate(f^(c/(b*x + a)^2)/x^2, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{f^{\frac{c}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{x^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f^(c/(b*x + a)^2)/x^2,x, algorithm="fricas")

[Out]

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

[Out]

Timed out

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GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{{\left (b x + a\right )}^{2}}}}{x^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f^(c/(b*x + a)^2)/x^2,x, algorithm="giac")

[Out]

integrate(f^(c/(b*x + a)^2)/x^2, x)