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

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{\log \left (a x^{-n}+b\right )}{c+d x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0257867, 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 = {} \[ \int \frac{\log \left (x^{-n} \left (a+b x^n\right )\right )}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Log[(a + b*x^n)/x^n]/(c + d*x),x]

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.470659, size = 0, normalized size = 0. \[ \int \frac{\log \left (x^{-n} \left (a+b x^n\right )\right )}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 1.703, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{dx+c}\ln \left ({\frac{a+b{x}^{n}}{{x}^{n}}} \right ) }\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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