3.3.29 \(\int \frac {f^{\frac {c}{(a+b x)^2}}}{x} \, dx\) [229]

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

[Out]

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

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Rubi [A]
time = 0.01, 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)^2}}}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[f^(c/(a + b*x)^2)/x,x]

[Out]

Defer[Int][f^(c/(a + b*x)^2)/x, x]

Rubi steps

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

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Mathematica [A]
time = 0.05, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {f^{\frac {c}{(a+b x)^2}}}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[f^(c/(a + b*x)^2)/x,x]

[Out]

Integrate[f^(c/(a + b*x)^2)/x, x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

integral(f^(c/(b^2*x^2 + 2*a*b*x + a^2))/x, 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 )^{2}}}}{x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

integrate(f^(c/(b*x + a)^2)/x, 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 )}^2}}}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(f^(c/(a + b*x)^2)/x,x)

[Out]

int(f^(c/(a + b*x)^2)/x, x)

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