3.73.57 \(\int \frac {24 x^2+24 x^2 \log (3)}{\log (3)} \, dx\)

Optimal. Leaf size=13 \[ 8 x^2 \left (x+\frac {x}{\log (3)}\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {6, 12, 30} \begin {gather*} \frac {8 x^3 (1+\log (3))}{\log (3)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(24*x^2 + 24*x^2*Log[3])/Log[3],x]

[Out]

(8*x^3*(1 + Log[3]))/Log[3]

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

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} &=\int \frac {x^2 (24+24 \log (3))}{\log (3)} \, dx\\ &=\frac {(24+24 \log (3)) \int x^2 \, dx}{\log (3)}\\ &=\frac {8 x^3 (1+\log (3))}{\log (3)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {8 x^3 (1+\log (3))}{\log (3)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(24*x^2 + 24*x^2*Log[3])/Log[3],x]

[Out]

(8*x^3*(1 + Log[3]))/Log[3]

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fricas [A]  time = 1.01, size = 16, normalized size = 1.23 \begin {gather*} \frac {8 \, {\left (x^{3} \log \relax (3) + x^{3}\right )}}{\log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x^2*log(3)+24*x^2)/log(3),x, algorithm="fricas")

[Out]

8*(x^3*log(3) + x^3)/log(3)

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giac [A]  time = 0.20, size = 16, normalized size = 1.23 \begin {gather*} \frac {8 \, {\left (x^{3} \log \relax (3) + x^{3}\right )}}{\log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x^2*log(3)+24*x^2)/log(3),x, algorithm="giac")

[Out]

8*(x^3*log(3) + x^3)/log(3)

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maple [A]  time = 0.02, size = 14, normalized size = 1.08

method	result	size
gosper	\(\frac {8 x^{3} \left (\ln \relax (3)+1\right )}{\ln \relax (3)}\)	\(14\)
norman	\(\frac {8 x^{3} \left (\ln \relax (3)+1\right )}{\ln \relax (3)}\)	\(14\)
risch	\(8 x^{3}+\frac {8 x^{3}}{\ln \relax (3)}\)	\(16\)
default	\(\frac {8 x^{3} \ln \relax (3)+8 x^{3}}{\ln \relax (3)}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*x^2*ln(3)+24*x^2)/ln(3),x,method=_RETURNVERBOSE)

[Out]

8*x^3*(ln(3)+1)/ln(3)

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maxima [A]  time = 0.34, size = 16, normalized size = 1.23 \begin {gather*} \frac {8 \, {\left (x^{3} \log \relax (3) + x^{3}\right )}}{\log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x^2*log(3)+24*x^2)/log(3),x, algorithm="maxima")

[Out]

8*(x^3*log(3) + x^3)/log(3)

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mupad [B]  time = 0.02, size = 14, normalized size = 1.08 \begin {gather*} \frac {x^3\,\left (8\,\ln \relax (3)+8\right )}{\ln \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*x^2*log(3) + 24*x^2)/log(3),x)

[Out]

(x^3*(8*log(3) + 8))/log(3)

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sympy [A]  time = 0.06, size = 12, normalized size = 0.92 \begin {gather*} \frac {x^{3} \left (8 + 8 \log {\relax (3 )}\right )}{\log {\relax (3 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x**2*ln(3)+24*x**2)/ln(3),x)

[Out]

x**3*(8 + 8*log(3))/log(3)

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