3.7.40 \(\int \frac {1}{a+b \log (c (d+\frac {e}{f+g x})^p)} \, dx\) [640]

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {1}{a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.00, 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}{a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.37, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{a+b \log \left (c \left (d+\frac {e}{f+g x}\right )^p\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {1}{a +b \ln \left (c \left (d +\frac {e}{g x +f}\right )^{p}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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