3.1.93 \(\int \frac {1}{(f+g x)^2 (a+b \log (c (d+e x)^n))} \, dx\) [93]

Optimal. Leaf size=27 \[ \text {Int}\left (\frac {1}{(f+g x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.02, 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 {1}{(f+g x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.36, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(f+g x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.16, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (g x +f \right )^{2} \left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {1}{{\left (f+g\,x\right )}^2\,\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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