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

Optimal. Leaf size=30 \[ \text{Unintegrable}\left (\frac{\log \left (d \left (\frac{1}{d}+f x^m\right )\right )}{x \left (a+b \log \left (c x^n\right )\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0400239, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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*}

Mathematica [A]  time = 0.0601192, size = 0, normalized size = 0. \[ \int \frac{\log \left (d \left (\frac{1}{d}+f x^m\right )\right )}{x \left (a+b \log \left (c x^n\right )\right )} \, dx \]

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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Maple [A]  time = 0.854, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( d \left ({d}^{-1}+f{x}^{m} \right ) \right ) }{x \left ( a+b\ln \left ( c{x}^{n} \right ) \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \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} \end{align*}

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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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left (d f x^{m} + 1\right )}{b x \log \left (c x^{n}\right ) + a x}, x\right ) \end{align*}

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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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

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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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \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} \end{align*}

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)