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

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

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Rubi [A]  time = 0.03, antiderivative size = 67, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\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} \end {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 62, normalized size = 0.93 \begin {gather*} -\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 {gather*}

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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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^3 (2+3 x)^5 (3+5 x)^2 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.96, size = 54, normalized size = 0.81 \begin {gather*} -\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 {gather*}

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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giac [A]  time = 0.96, size = 54, normalized size = 0.81 \begin {gather*} -\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 {gather*}

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

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maple [A]  time = 0.00, size = 55, normalized size = 0.82 \begin {gather*} -\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 {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(3*x+2)^5*(5*x+3)^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 = 0.49, size = 54, normalized size = 0.81 \begin {gather*} -\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 {gather*}

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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mupad [B]  time = 0.05, size = 54, normalized size = 0.81 \begin {gather*} -\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 {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(2*x - 1)^3*(3*x + 2)^5*(5*x + 3)^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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sympy [A]  time = 0.08, size = 60, normalized size = 0.90 \begin {gather*} - \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 {gather*}

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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