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

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

[Out]

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

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Rubi [A]  time = 0.0700657, 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. \[ \text{Int}\left (\frac{f^{c (a+b x)^n}}{x^2},x\right ) \]

Verification is Not applicable to the result.

[In]  Int[f^(c*(a + b*x)^n)/x^2,x]

[Out]

Defer[Int][f^(c*(a + b*x)^n)/x^2, x]

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Integral(f**(c*(a + b*x)**n)/x**2, x)

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Mathematica [A]  time = 0.0328274, size = 0, normalized size = 0. \[ \int \frac{f^{c (a+b x)^n}}{x^2} \, dx \]

Verification is Not applicable to the result.

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

[Out]

Integrate[f^(c*(a + b*x)^n)/x^2, x]

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Maple [A]  time = 0.061, size = 0, normalized size = 0. \[ \int{\frac{{f}^{c \left ( bx+a \right ) ^{n}}}{{x}^{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(f^(c*(b*x+a)^n)/x^2,x)

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate(f^((b*x + a)^n*c)/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integral(f^((b*x + a)^n*c)/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

Integral(f**(c*(a + b*x)**n)/x**2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate(f^((b*x + a)^n*c)/x^2, x)