3.3.38 \(\int \frac {f^{\frac {c}{(a+b x)^3}}}{x^2} \, dx\) [238]

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

[Out]

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

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Rubi [A]
time = 0.03, 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 = {} \begin {gather*} \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[f^(c/(a + b*x)^3)/x^2,x]

[Out]

Defer[Int][f^(c/(a + b*x)^3)/x^2, x]

Rubi steps

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

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Mathematica [A]
time = 0.18, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {f^{\frac {c}{(a+b x)^3}}}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[f^(c/(a + b*x)^3)/x^2,x]

[Out]

Integrate[f^(c/(a + b*x)^3)/x^2, x]

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Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {f^{\frac {c}{\left (b x +a \right )^{3}}}}{x^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^(c/(b*x + a)^3)/x^2, x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(f^(c/(b*x+a)^3)/x^2,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^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(f**(c/(a + b*x)**3)/x**2, x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(f^(c/(b*x + a)^3)/x^2, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(c/(a + b*x)^3)/x^2,x)

[Out]

int(f^(c/(a + b*x)^3)/x^2, x)

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