3.1358 \(\int (1-2 x)^3 (2+3 x)^5 (3+5 x)^2 \, dx\)

Optimal. Leaf size=67 \[ -\frac{200 (3 x+2)^{11}}{8019}+\frac{218}{729} (3 x+2)^{10}-\frac{8198 (3 x+2)^9}{6561}+\frac{11599 (3 x+2)^8}{5832}-\frac{532}{729} (3 x+2)^7+\frac{343 (3 x+2)^6}{4374} \]

[Out]

(343*(2 + 3*x)^6)/4374 - (532*(2 + 3*x)^7)/729 + (11599*(2 + 3*x)^8)/5832 - (8198*(2 + 3*x)^9)/6561 + (218*(2
+ 3*x)^10)/729 - (200*(2 + 3*x)^11)/8019

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Rubi [A]  time = 0.0291802, antiderivative size = 67, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{200 (3 x+2)^{11}}{8019}+\frac{218}{729} (3 x+2)^{10}-\frac{8198 (3 x+2)^9}{6561}+\frac{11599 (3 x+2)^8}{5832}-\frac{532}{729} (3 x+2)^7+\frac{343 (3 x+2)^6}{4374} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x)^2,x]

[Out]

(343*(2 + 3*x)^6)/4374 - (532*(2 + 3*x)^7)/729 + (11599*(2 + 3*x)^8)/5832 - (8198*(2 + 3*x)^9)/6561 + (218*(2
+ 3*x)^10)/729 - (200*(2 + 3*x)^11)/8019

Rule 88

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))

Rubi steps

\begin{align*} \int (1-2 x)^3 (2+3 x)^5 (3+5 x)^2 \, dx &=\int \left (\frac{343}{243} (2+3 x)^5-\frac{3724}{243} (2+3 x)^6+\frac{11599}{243} (2+3 x)^7-\frac{8198}{243} (2+3 x)^8+\frac{2180}{243} (2+3 x)^9-\frac{200}{243} (2+3 x)^{10}\right ) \, dx\\ &=\frac{343 (2+3 x)^6}{4374}-\frac{532}{729} (2+3 x)^7+\frac{11599 (2+3 x)^8}{5832}-\frac{8198 (2+3 x)^9}{6561}+\frac{218}{729} (2+3 x)^{10}-\frac{200 (2+3 x)^{11}}{8019}\\ \end{align*}

Mathematica [A]  time = 0.0023714, size = 62, normalized size = 0.93 \[ -\frac{48600 x^{11}}{11}-14742 x^{10}-14874 x^9+\frac{21159 x^8}{8}+14334 x^7+\frac{39347 x^6}{6}-3486 x^5-3606 x^4-\frac{784 x^3}{3}+696 x^2+288 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(2 + 3*x)^5*(3 + 5*x)^2,x]

[Out]

288*x + 696*x^2 - (784*x^3)/3 - 3606*x^4 - 3486*x^5 + (39347*x^6)/6 + 14334*x^7 + (21159*x^8)/8 - 14874*x^9 -
14742*x^10 - (48600*x^11)/11

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Maple [A]  time = 0.001, size = 55, normalized size = 0.8 \begin{align*} -{\frac{48600\,{x}^{11}}{11}}-14742\,{x}^{10}-14874\,{x}^{9}+{\frac{21159\,{x}^{8}}{8}}+14334\,{x}^{7}+{\frac{39347\,{x}^{6}}{6}}-3486\,{x}^{5}-3606\,{x}^{4}-{\frac{784\,{x}^{3}}{3}}+696\,{x}^{2}+288\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(2+3*x)^5*(3+5*x)^2,x)

[Out]

-48600/11*x^11-14742*x^10-14874*x^9+21159/8*x^8+14334*x^7+39347/6*x^6-3486*x^5-3606*x^4-784/3*x^3+696*x^2+288*
x

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Maxima [A]  time = 1.01515, size = 73, normalized size = 1.09 \begin{align*} -\frac{48600}{11} \, x^{11} - 14742 \, x^{10} - 14874 \, x^{9} + \frac{21159}{8} \, x^{8} + 14334 \, x^{7} + \frac{39347}{6} \, x^{6} - 3486 \, x^{5} - 3606 \, x^{4} - \frac{784}{3} \, x^{3} + 696 \, x^{2} + 288 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^5*(3+5*x)^2,x, algorithm="maxima")

[Out]

-48600/11*x^11 - 14742*x^10 - 14874*x^9 + 21159/8*x^8 + 14334*x^7 + 39347/6*x^6 - 3486*x^5 - 3606*x^4 - 784/3*
x^3 + 696*x^2 + 288*x

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Fricas [A]  time = 1.05509, size = 180, normalized size = 2.69 \begin{align*} -\frac{48600}{11} x^{11} - 14742 x^{10} - 14874 x^{9} + \frac{21159}{8} x^{8} + 14334 x^{7} + \frac{39347}{6} x^{6} - 3486 x^{5} - 3606 x^{4} - \frac{784}{3} x^{3} + 696 x^{2} + 288 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^5*(3+5*x)^2,x, algorithm="fricas")

[Out]

-48600/11*x^11 - 14742*x^10 - 14874*x^9 + 21159/8*x^8 + 14334*x^7 + 39347/6*x^6 - 3486*x^5 - 3606*x^4 - 784/3*
x^3 + 696*x^2 + 288*x

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Sympy [A]  time = 0.071187, size = 60, normalized size = 0.9 \begin{align*} - \frac{48600 x^{11}}{11} - 14742 x^{10} - 14874 x^{9} + \frac{21159 x^{8}}{8} + 14334 x^{7} + \frac{39347 x^{6}}{6} - 3486 x^{5} - 3606 x^{4} - \frac{784 x^{3}}{3} + 696 x^{2} + 288 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**3*(2+3*x)**5*(3+5*x)**2,x)

[Out]

-48600*x**11/11 - 14742*x**10 - 14874*x**9 + 21159*x**8/8 + 14334*x**7 + 39347*x**6/6 - 3486*x**5 - 3606*x**4
- 784*x**3/3 + 696*x**2 + 288*x

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Giac [A]  time = 2.42765, size = 73, normalized size = 1.09 \begin{align*} -\frac{48600}{11} \, x^{11} - 14742 \, x^{10} - 14874 \, x^{9} + \frac{21159}{8} \, x^{8} + 14334 \, x^{7} + \frac{39347}{6} \, x^{6} - 3486 \, x^{5} - 3606 \, x^{4} - \frac{784}{3} \, x^{3} + 696 \, x^{2} + 288 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^5*(3+5*x)^2,x, algorithm="giac")

[Out]

-48600/11*x^11 - 14742*x^10 - 14874*x^9 + 21159/8*x^8 + 14334*x^7 + 39347/6*x^6 - 3486*x^5 - 3606*x^4 - 784/3*
x^3 + 696*x^2 + 288*x