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

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 = 0.09, 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 = {} \[ \int \frac {\log ^q\left (c \left (d+e x^n\right )^p\right )}{x \left (f+g x^n\right )} \, dx \]

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 = 1.96, size = 0, normalized size = 0.00 \[ \int \frac {\log ^q\left (c \left (d+e x^n\right )^p\right )}{x \left (f+g x^n\right )} \, dx \]

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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fricas [A]  time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left ({\left (e x^{n} + d\right )}^{p} c\right )^{q}}{g x x^{n} + f x}, x\right ) \]

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

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

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

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maple [A]  time = 19.94, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (c \left (e \,x^{n}+d \right )^{p}\right )^{q}}{\left (g \,x^{n}+f \right ) x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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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