3.161 \(\int \frac{1}{x^2 (d+e x) (a+b \log (c x^n))} \, dx\)

Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )},x\right ) \]

[Out]

Unintegrable[1/(x^2*(d + e*x)*(a + b*Log[c*x^n])), x]

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Rubi [A]  time = 0.0890865, 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 = {} \[ \int \frac{1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x^2*(d + e*x)*(a + b*Log[c*x^n])),x]

[Out]

Defer[Int][1/(x^2*(d + e*x)*(a + b*Log[c*x^n])), x]

Rubi steps

\begin{align*} \int \frac{1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx &=\int \frac{1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx\\ \end{align*}

Mathematica [A]  time = 0.614304, size = 0, normalized size = 0. \[ \int \frac{1}{x^2 (d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x^2*(d + e*x)*(a + b*Log[c*x^n])),x]

[Out]

Integrate[1/(x^2*(d + e*x)*(a + b*Log[c*x^n])), x]

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Maple [A]  time = 0.516, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{2} \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(1/x^2/(e*x+d)/(a+b*ln(c*x^n)),x)

[Out]

int(1/x^2/(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{1}{{\left (e x + d\right )}{\left (b \log \left (c x^{n}\right ) + a\right )} x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/(e*x+d)/(a+b*log(c*x^n)),x, algorithm="maxima")

[Out]

integrate(1/((e*x + d)*(b*log(c*x^n) + a)*x^2), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{a e x^{3} + a d x^{2} +{\left (b e x^{3} + b d x^{2}\right )} \log \left (c x^{n}\right )}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/(e*x+d)/(a+b*log(c*x^n)),x, algorithm="fricas")

[Out]

integral(1/(a*e*x^3 + a*d*x^2 + (b*e*x^3 + b*d*x^2)*log(c*x^n)), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{2} \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(1/x**2/(e*x+d)/(a+b*ln(c*x**n)),x)

[Out]

Integral(1/(x**2*(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{1}{{\left (e x + d\right )}{\left (b \log \left (c x^{n}\right ) + a\right )} x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/(e*x+d)/(a+b*log(c*x^n)),x, algorithm="giac")

[Out]

integrate(1/((e*x + d)*(b*log(c*x^n) + a)*x^2), x)