3.239 \(\int \frac{f^{\frac{c}{(a+b x)^3}}}{x^3} \, dx\)

Optimal. Leaf size=18 \[ \text{Int}\left (\frac{f^{\frac{c}{(a+b x)^3}}}{x^3},x\right ) \]

[Out]

CannotIntegrate[f^(c/(a + b*x)^3)/x^3, x]

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Rubi [A]  time = 0.0609952, 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. \[ \text{Int}\left (\frac{f^{\frac{c}{(a+b x)^3}}}{x^3},x\right ) \]

Verification is Not applicable to the result.

[In]  Int[f^(c/(a + b*x)^3)/x^3,x]

[Out]

Defer[Int][f^(c/(a + b*x)^3)/x^3, x]

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Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{\left (a + b x\right )^{3}}}}{x^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(f**(c/(b*x+a)**3)/x**3,x)

[Out]

Integral(f**(c/(a + b*x)**3)/x**3, x)

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Mathematica [A]  time = 0.040339, size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{(a+b x)^3}}}{x^3} \, dx \]

Verification is Not applicable to the result.

[In]  Integrate[f^(c/(a + b*x)^3)/x^3,x]

[Out]

Integrate[f^(c/(a + b*x)^3)/x^3, x]

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Maple [A]  time = 0.056, size = 0, normalized size = 0. \[ \int{\frac{1}{{x}^{3}}{f}^{{\frac{c}{ \left ( bx+a \right ) ^{3}}}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(f^(c/(b*x+a)^3)/x^3,x)

[Out]

int(f^(c/(b*x+a)^3)/x^3,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{{\left (b x + a\right )}^{3}}}}{x^{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f^(c/(b*x + a)^3)/x^3,x, algorithm="maxima")

[Out]

integrate(f^(c/(b*x + a)^3)/x^3, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{f^{\frac{c}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}}}{x^{3}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f^(c/(b*x + a)^3)/x^3,x, algorithm="fricas")

[Out]

integral(f^(c/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3))/x^3, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{\left (a + b x\right )^{3}}}}{x^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f**(c/(b*x+a)**3)/x**3,x)

[Out]

Integral(f**(c/(a + b*x)**3)/x**3, x)

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GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{{\left (b x + a\right )}^{3}}}}{x^{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(f^(c/(b*x + a)^3)/x^3,x, algorithm="giac")

[Out]

integrate(f^(c/(b*x + a)^3)/x^3, x)