3.14.76 \(\int \frac {6 x^5}{\log ^2(-20+e^{24})} \, dx\)

Optimal. Leaf size=12 \[ \frac {x^6}{\log ^2\left (-20+e^{24}\right )} \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 30} \begin {gather*} \frac {x^6}{\log ^2\left (e^{24}-20\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(6*x^5)/Log[-20 + E^24]^2,x]

[Out]

x^6/Log[-20 + E^24]^2

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {6 \int x^5 \, dx}{\log ^2\left (-20+e^{24}\right )}\\ &=\frac {x^6}{\log ^2\left (-20+e^{24}\right )}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} \frac {x^6}{\log ^2\left (-20+e^{24}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(6*x^5)/Log[-20 + E^24]^2,x]

[Out]

x^6/Log[-20 + E^24]^2

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fricas [A]  time = 0.79, size = 11, normalized size = 0.92 \begin {gather*} \frac {x^{6}}{\log \left (e^{24} - 20\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x^5/log(exp(24)-20)^2,x, algorithm="fricas")

[Out]

x^6/log(e^24 - 20)^2

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giac [A]  time = 0.36, size = 11, normalized size = 0.92 \begin {gather*} \frac {x^{6}}{\log \left (e^{24} - 20\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x^5/log(exp(24)-20)^2,x, algorithm="giac")

[Out]

x^6/log(e^24 - 20)^2

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maple [A]  time = 0.03, size = 12, normalized size = 1.00

method	result	size
gosper	\(\frac {x^{6}}{\ln \left ({\mathrm e}^{24}-20\right )^{2}}\)	\(12\)
default	\(\frac {x^{6}}{\ln \left ({\mathrm e}^{24}-20\right )^{2}}\)	\(12\)
norman	\(\frac {x^{6}}{\ln \left ({\mathrm e}^{24}-20\right )^{2}}\)	\(12\)
risch	\(\frac {x^{6}}{\ln \left ({\mathrm e}^{24}-20\right )^{2}}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(6*x^5/ln(exp(24)-20)^2,x,method=_RETURNVERBOSE)

[Out]

x^6/ln(exp(24)-20)^2

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maxima [A]  time = 0.52, size = 11, normalized size = 0.92 \begin {gather*} \frac {x^{6}}{\log \left (e^{24} - 20\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x^5/log(exp(24)-20)^2,x, algorithm="maxima")

[Out]

x^6/log(e^24 - 20)^2

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mupad [B]  time = 0.03, size = 11, normalized size = 0.92 \begin {gather*} \frac {x^6}{{\ln \left ({\mathrm {e}}^{24}-20\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((6*x^5)/log(exp(24) - 20)^2,x)

[Out]

x^6/log(exp(24) - 20)^2

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sympy [A]  time = 0.05, size = 10, normalized size = 0.83 \begin {gather*} \frac {x^{6}}{\log {\left (-20 + e^{24} \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(6*x**5/ln(exp(24)-20)**2,x)

[Out]

x**6/log(-20 + exp(24))**2

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