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

Optimal. Leaf size=13 $$8x^2(x+\frac{x}{\log (3)})$$

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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} $$\begin{array}{c}\frac{8x^3(1+\log (3))}{\log (3)}\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{x^2(24+24\log (3))}{\log (3)}dx\\ & =\frac{(24+24\log (3))\int x^{2}dx}{\log (3)}\\ & =\frac{8x^3(1+\log (3))}{\log (3)}\end{array}\end{array}$$

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

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 $$\begin{array}{c}\frac{8(x^3\log (3)+x^3)}{\log (3)}\end{array}$$

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 $$\begin{array}{c}\frac{8(x^3\log (3)+x^3)}{\log (3)}\end{array}$$

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	$\frac{8x^3(\ln (3)+1)}{\ln (3)}$	$14$
norman	$\frac{8x^3(\ln (3)+1)}{\ln (3)}$	$14$
risch	$8x^3+\frac{8x^3}{\ln (3)}$	$16$
default	$\frac{8x^3\ln (3)+8x^3}{\ln (3)}$	$19$

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 $$\begin{array}{c}\frac{8(x^3\log (3)+x^3)}{\log (3)}\end{array}$$

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 $$\begin{array}{c}\frac{x^3(8\ln (3)+8)}{\ln (3)}\end{array}$$

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 $$\begin{array}{c}\frac{x^3(8+8\log (3))}{\log (3)}\end{array}$$

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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