3.7.2 \(\int x (a+b \log (c (d+\frac {e}{x^{2/3}})^2))^p \, dx\) [602]

Optimal. Leaf size=25 \[ \text {Int}\left (x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^2\right )\right )^p,x\right ) \]

[Out]

Unintegrable(x*(a+b*ln(c*(d+e/x^(2/3))^2))^p,x)

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Rubi [A]
time = 0.03, 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 = {} \begin {gather*} \int x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^2\right )\right )^p \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x*(a + b*Log[c*(d + e/x^(2/3))^2])^p,x]

[Out]

3*Defer[Subst][Defer[Int][x^5*(a + b*Log[c*(d + e/x^2)^2])^p, x], x, x^(1/3)]

Rubi steps

\begin {align*} \int x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^2\right )\right )^p \, dx &=3 \text {Subst}\left (\int x^5 \left (a+b \log \left (c \left (d+\frac {e}{x^2}\right )^2\right )\right )^p \, dx,x,\sqrt [3]{x}\right )\\ \end {align*}

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Mathematica [A]
time = 0.19, size = 0, normalized size = 0.00 \begin {gather*} \int x \left (a+b \log \left (c \left (d+\frac {e}{x^{2/3}}\right )^2\right )\right )^p \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[x*(a + b*Log[c*(d + e/x^(2/3))^2])^p,x]

[Out]

Integrate[x*(a + b*Log[c*(d + e/x^(2/3))^2])^p, x]

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Maple [A]
time = 0.00, size = 0, normalized size = 0.00 \[\int x \left (a +b \ln \left (c \left (d +\frac {e}{x^{\frac {2}{3}}}\right )^{2}\right )\right )^{p}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x*(a+b*ln(c*(d+e/x^(2/3))^2))^p,x)

[Out]

int(x*(a+b*ln(c*(d+e/x^(2/3))^2))^p,x)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(a+b*log(c*(d+e/x^(2/3))^2))^p,x, algorithm="maxima")

[Out]

integrate((b*log(c*(d + e/x^(2/3))^2) + a)^p*x, x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(a+b*log(c*(d+e/x^(2/3))^2))^p,x, algorithm="fricas")

[Out]

integral((b*log((c*d^2*x^2 + 2*c*d*x^(4/3)*e + c*x^(2/3)*e^2)/x^2) + a)^p*x, x)

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(a+b*ln(c*(d+e/x**(2/3))**2))**p,x)

[Out]

Timed out

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(a+b*log(c*(d+e/x^(2/3))^2))^p,x, algorithm="giac")

[Out]

integrate((b*log(c*(d + e/x^(2/3))^2) + a)^p*x, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int x\,{\left (a+b\,\ln \left (c\,{\left (d+\frac {e}{x^{2/3}}\right )}^2\right )\right )}^p \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x*(a + b*log(c*(d + e/x^(2/3))^2))^p,x)

[Out]

int(x*(a + b*log(c*(d + e/x^(2/3))^2))^p, x)

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