3.231 \(\int \frac {f^{\frac {c}{(a+b x)^2}}}{x^3} \, dx\)

Optimal. Leaf size=18 \[ \text {Int}\left (\frac {f^{\frac {c}{(a+b x)^2}}}{x^3},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {f^{\frac {c}{(a+b x)^2}}}{x^3} \, dx \]

Verification is Not applicable to the result.

[In]

Int[f^(c/(a + b*x)^2)/x^3,x]

[Out]

Defer[Int][f^(c/(a + b*x)^2)/x^3, x]

Rubi steps

\begin {align*} \int \frac {f^{\frac {c}{(a+b x)^2}}}{x^3} \, dx &=\int \frac {f^{\frac {c}{(a+b x)^2}}}{x^3} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.29, size = 0, normalized size = 0.00 \[ \int \frac {f^{\frac {c}{(a+b x)^2}}}{x^3} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[f^(c/(a + b*x)^2)/x^3,x]

[Out]

Integrate[f^(c/(a + b*x)^2)/x^3, x]

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fricas [A]  time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {f^{\frac {c}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{x^{3}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(f^(c/(b*x+a)^2)/x^3,x, algorithm="fricas")

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{\frac {c}{{\left (b x + a\right )}^{2}}}}{x^{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(f^(c/(b*x+a)^2)/x^3,x, algorithm="giac")

[Out]

integrate(f^(c/(b*x + a)^2)/x^3, x)

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maple [A]  time = 0.10, size = 0, normalized size = 0.00 \[ \int \frac {f^{\frac {c}{\left (b x +a \right )^{2}}}}{x^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(1/(b*x+a)^2*c)/x^3,x)

[Out]

int(f^(1/(b*x+a)^2*c)/x^3,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{\frac {c}{{\left (b x + a\right )}^{2}}}}{x^{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(f^(c/(b*x+a)^2)/x^3,x, algorithm="maxima")

[Out]

integrate(f^(c/(b*x + a)^2)/x^3, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {f^{\frac {c}{{\left (a+b\,x\right )}^2}}}{x^3} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(c/(a + b*x)^2)/x^3,x)

[Out]

int(f^(c/(a + b*x)^2)/x^3, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f^{\frac {c}{\left (a + b x\right )^{2}}}}{x^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(f**(c/(a + b*x)**2)/x**3, x)

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