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

Optimal. Leaf size=24 \[ \text {Int}\left (\frac {x}{(d+e x) \left (a+b \log \left (c x^n\right )\right )},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.06, 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 = {} \[ \int \frac {x}{(d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx \]

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*}

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Mathematica [A]  time = 0.76, size = 0, normalized size = 0.00 \[ \int \frac {x}{(d+e x) \left (a+b \log \left (c x^n\right )\right )} \, dx \]

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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fricas [A]  time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x}{a e x + a d + {\left (b e x + b d\right )} \log \left (c x^{n}\right )}, x\right ) \]

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

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)

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maple [A]  time = 0.51, size = 0, normalized size = 0.00 \[ \int \frac {x}{\left (e x +d \right ) \left (b \ln \left (c \,x^{n}\right )+a \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x}{\left (a+b\,\ln \left (c\,x^n\right )\right )\,\left (d+e\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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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