3.560 \(\int \frac {(a+b \log (c (d+e \sqrt [3]{x})))^p}{x} \, dx\)

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )\right )\right )^p}{x},x\right ) \]

[Out]

Unintegrable((a+b*ln(c*(d+e*x^(1/3))))^p/x,x)

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Rubi [A]  time = 0.05, 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 = {} \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )\right )\right )^p}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(a + b*Log[c*(d + e*x^(1/3))])^p/x,x]

[Out]

3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x)])^p/x, x], x, x^(1/3)]

Rubi steps

\begin {align*} \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )\right )\right )^p}{x} \, dx &=3 \operatorname {Subst}\left (\int \frac {(a+b \log (c (d+e x)))^p}{x} \, dx,x,\sqrt [3]{x}\right )\\ \end {align*}

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Mathematica [A]  time = 0.26, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+b \log \left (c \left (d+e \sqrt [3]{x}\right )\right )\right )^p}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(a + b*Log[c*(d + e*x^(1/3))])^p/x,x]

[Out]

Integrate[(a + b*Log[c*(d + e*x^(1/3))])^p/x, x]

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fricas [A]  time = 0.66, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b \log \left (c e x^{\frac {1}{3}} + c d\right ) + a\right )}^{p}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*log(c*(d+e*x^(1/3))))^p/x,x, algorithm="fricas")

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left ({\left (e x^{\frac {1}{3}} + d\right )} c\right ) + a\right )}^{p}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*log(c*(d+e*x^(1/3))))^p/x,x, algorithm="giac")

[Out]

integrate((b*log((e*x^(1/3) + d)*c) + a)^p/x, x)

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maple [A]  time = 0.08, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (\left (e \,x^{\frac {1}{3}}+d \right ) c \right )+a \right )^{p}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*ln((e*x^(1/3)+d)*c)+a)^p/x,x)

[Out]

int((b*ln((e*x^(1/3)+d)*c)+a)^p/x,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left ({\left (e x^{\frac {1}{3}} + d\right )} c\right ) + a\right )}^{p}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*log(c*(d+e*x^(1/3))))^p/x,x, algorithm="maxima")

[Out]

integrate((b*log((e*x^(1/3) + d)*c) + a)^p/x, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (a+b\,\ln \left (c\,\left (d+e\,x^{1/3}\right )\right )\right )}^p}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*log(c*(d + e*x^(1/3))))^p/x,x)

[Out]

int((a + b*log(c*(d + e*x^(1/3))))^p/x, x)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*ln(c*(d+e*x**(1/3))))**p/x,x)

[Out]

Timed out

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