3.137 \(\int \frac{1}{(f+g x) (a+b \log (c (d+e x)^n))^{5/2}} \, dx\)

Optimal. Leaf size=28 \[ \text{Unintegrable}\left (\frac{1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}},x\right ) \]

[Out]

Unintegrable[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(5/2)), x]

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Rubi [A]  time = 0.0587893, 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., Rules used = {} \[ \int \frac{1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(5/2)),x]

[Out]

Defer[Int][1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(5/2)), x]

Rubi steps

\begin{align*} \int \frac{1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}} \, dx &=\int \frac{1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}} \, dx\\ \end{align*}

Mathematica [A]  time = 0.552144, size = 0, normalized size = 0. \[ \int \frac{1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(5/2)),x]

[Out]

Integrate[1/((f + g*x)*(a + b*Log[c*(d + e*x)^n])^(5/2)), x]

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Maple [A]  time = 0.97, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{gx+f} \left ( a+b\ln \left ( c \left ( ex+d \right ) ^{n} \right ) \right ) ^{-{\frac{5}{2}}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(g*x+f)/(a+b*ln(c*(e*x+d)^n))^(5/2),x)

[Out]

int(1/(g*x+f)/(a+b*ln(c*(e*x+d)^n))^(5/2),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (g x + f\right )}{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{\frac{5}{2}}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(g*x+f)/(a+b*log(c*(e*x+d)^n))^(5/2),x, algorithm="maxima")

[Out]

integrate(1/((g*x + f)*(b*log((e*x + d)^n*c) + a)^(5/2)), x)

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Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(g*x+f)/(a+b*log(c*(e*x+d)^n))^(5/2),x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(g*x+f)/(a+b*ln(c*(e*x+d)**n))**(5/2),x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (g x + f\right )}{\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{\frac{5}{2}}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(g*x+f)/(a+b*log(c*(e*x+d)^n))^(5/2),x, algorithm="giac")

[Out]

integrate(1/((g*x + f)*(b*log((e*x + d)^n*c) + a)^(5/2)), x)