3.4.86 \(\int \frac {\log ^q(c (d+e x^n)^p)}{x (f+g x^n)} \, dx\) [386]

Optimal. Leaf size=30 \[ \text {Int}\left (\frac {\log ^q\left (c \left (d+e x^n\right )^p\right )}{x \left (f+g x^n\right )},x\right ) \]

[Out]

Unintegrable(ln(c*(d+e*x^n)^p)^q/x/(f+g*x^n),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 = {} \begin {gather*} \int \frac {\log ^q\left (c \left (d+e x^n\right )^p\right )}{x \left (f+g x^n\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Log[c*(d + e*x^n)^p]^q/(x*(f + g*x^n)),x]

[Out]

Defer[Int][Log[c*(d + e*x^n)^p]^q/(x*(f + g*x^n)), x]

Rubi steps

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

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Mathematica [A]
time = 1.16, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log ^q\left (c \left (d+e x^n\right )^p\right )}{x \left (f+g x^n\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Log[c*(d + e*x^n)^p]^q/(x*(f + g*x^n)),x]

[Out]

Integrate[Log[c*(d + e*x^n)^p]^q/(x*(f + g*x^n)), x]

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Maple [A]
time = 0.70, size = 0, normalized size = 0.00 \[\int \frac {\ln \left (c \left (d +e \,x^{n}\right )^{p}\right )^{q}}{x \left (f +g \,x^{n}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(c*(d+e*x^n)^p)^q/x/(f+g*x^n),x)

[Out]

int(ln(c*(d+e*x^n)^p)^q/x/(f+g*x^n),x)

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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(c*(d+e*x^n)^p)^q/x/(f+g*x^n),x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not
of the expected type LIST

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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(log(c*(d+e*x^n)^p)^q/x/(f+g*x^n),x, algorithm="fricas")

[Out]

integral(log((x^n*e + d)^p*c)^q/(g*x*x^n + f*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(c*(d+e*x**n)**p)**q/x/(f+g*x**n),x)

[Out]

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

[Out]

integrate(log((x^n*e + d)^p*c)^q/((g*x^n + f)*x), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\ln \left (c\,{\left (d+e\,x^n\right )}^p\right )}^q}{x\,\left (f+g\,x^n\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(c*(d + e*x^n)^p)^q/(x*(f + g*x^n)),x)

[Out]

int(log(c*(d + e*x^n)^p)^q/(x*(f + g*x^n)), x)

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