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

Optimal. Leaf size=29 \[ \text {Int}\left (\frac {1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.06, 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 = {} \[ \int \frac {1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}} \, dx \]

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*}

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Mathematica [A]  time = 0.56, size = 0, normalized size = 0.00 \[ \int \frac {1}{(f+g x) \left (a+b \log \left (c (d+e x)^n\right )\right )^{5/2}} \, dx \]

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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fricas [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

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: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (g x + f\right )} {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{\frac {5}{2}}}\,{d x} \]

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)

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maple [A]  time = 0.55, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (g x +f \right ) \left (b \ln \left (c \left (e x +d \right )^{n}\right )+a \right )^{\frac {5}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (g x + f\right )} {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{\frac {5}{2}}}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {1}{\left (f+g\,x\right )\,{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^{5/2}} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

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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