3.158 \(\int \frac{x}{(d+e x) (a+b \log (c x^n))} \, dx\)

Optimal. Leaf size=23 \[ \text{Unintegrable}\left (\frac{x}{(d+e x) \left (a+b \log \left (c x^n\right )\right )},x\right ) \]

[Out]

Unintegrable[x/((d + e*x)*(a + b*Log[c*x^n])), x]

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Rubi [A]  time = 0.0605134, 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 = {} \[ \int \frac{x}{(d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[x/((d + e*x)*(a + b*Log[c*x^n])),x]

[Out]

Defer[Int][x/((d + e*x)*(a + b*Log[c*x^n])), x]

Rubi steps

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

Mathematica [A]  time = 0.708518, size = 0, normalized size = 0. \[ \int \frac{x}{(d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x/((d + e*x)*(a + b*Log[c*x^n])),x]

[Out]

Integrate[x/((d + e*x)*(a + b*Log[c*x^n])), x]

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Maple [A]  time = 0.51, size = 0, normalized size = 0. \begin{align*} \int{\frac{x}{ \left ( ex+d \right ) \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(x/(e*x+d)/(a+b*ln(c*x^n)),x)

[Out]

int(x/(e*x+d)/(a+b*ln(c*x^n)),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{{\left (e x + d\right )}{\left (b \log \left (c x^{n}\right ) + a\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x/((e*x + d)*(b*log(c*x^n) + a)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(x/(a*e*x + a*d + (b*e*x + b*d)*log(c*x^n)), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{\left (a + b \log{\left (c x^{n} \right )}\right ) \left (d + e x\right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(e*x+d)/(a+b*ln(c*x**n)),x)

[Out]

Integral(x/((a + b*log(c*x**n))*(d + e*x)), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{{\left (e x + d\right )}{\left (b \log \left (c x^{n}\right ) + a\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x/((e*x + d)*(b*log(c*x^n) + a)), x)