3.68 \(\int \frac {\log (d (\frac {1}{d}+f x^m))}{x (a+b \log (c x^n))} \, dx\)

Optimal. Leaf size=31 \[ \text {Int}\left (\frac {\log \left (d \left (\frac {1}{d}+f x^m\right )\right )}{x \left (a+b \log \left (c x^n\right )\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.04, 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 = {} \[ \int \frac {\log \left (d \left (\frac {1}{d}+f x^m\right )\right )}{x \left (a+b \log \left (c x^n\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])),x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.06, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (d \left (\frac {1}{d}+f x^m\right )\right )}{x \left (a+b \log \left (c x^n\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])),x]

[Out]

Integrate[Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])), x]

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fricas [A]  time = 0.90, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left (d f x^{m} + 1\right )}{b x \log \left (c x^{n}\right ) + a x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(d*(1/d+f*x^m))/x/(a+b*log(c*x^n)),x, algorithm="giac")

[Out]

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

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maple [A]  time = 1.80, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (\left (f \,x^{m}+\frac {1}{d}\right ) d \right )}{\left (b \ln \left (c \,x^{n}\right )+a \right ) x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(d*(1/d+f*x^m))/x/(a+b*log(c*x^n)),x, algorithm="maxima")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(log(d*(f*x^m + 1/d))/(x*(a + b*log(c*x^n))), 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(ln(d*(1/d+f*x**m))/x/(a+b*ln(c*x**n)),x)

[Out]

Timed out

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