3.1275 \(\int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{500 (3 x+2)^{11}}{8019}-\frac{380}{729} (3 x+2)^{10}+\frac{8285 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{5832}+\frac{109}{729} (3 x+2)^7-\frac{49 (3 x+2)^6}{4374} \]

[Out]

(-49*(2 + 3*x)^6)/4374 + (109*(2 + 3*x)^7)/729 - (4099*(2 + 3*x)^8)/5832 + (8285*(2 + 3*x)^9)/6561 - (380*(2 +
3*x)^10)/729 + (500*(2 + 3*x)^11)/8019

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Rubi [A]  time = 0.0293167, 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} \[ \frac{500 (3 x+2)^{11}}{8019}-\frac{380}{729} (3 x+2)^{10}+\frac{8285 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{5832}+\frac{109}{729} (3 x+2)^7-\frac{49 (3 x+2)^6}{4374} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(-49*(2 + 3*x)^6)/4374 + (109*(2 + 3*x)^7)/729 - (4099*(2 + 3*x)^8)/5832 + (8285*(2 + 3*x)^9)/6561 - (380*(2 +
3*x)^10)/729 + (500*(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)^2 (2+3 x)^5 (3+5 x)^3 \, dx &=\int \left (-\frac{49}{243} (2+3 x)^5+\frac{763}{243} (2+3 x)^6-\frac{4099}{243} (2+3 x)^7+\frac{8285}{243} (2+3 x)^8-\frac{3800}{243} (2+3 x)^9+\frac{500}{243} (2+3 x)^{10}\right ) \, dx\\ &=-\frac{49 (2+3 x)^6}{4374}+\frac{109}{729} (2+3 x)^7-\frac{4099 (2+3 x)^8}{5832}+\frac{8285 (2+3 x)^9}{6561}-\frac{380}{729} (2+3 x)^{10}+\frac{500 (2+3 x)^{11}}{8019}\\ \end{align*}

Mathematica [A]  time = 0.0023325, size = 60, normalized size = 0.9 \[ \frac{121500 x^{11}}{11}+50220 x^{10}+89655 x^9+\frac{551349 x^8}{8}-987 x^7-\frac{252329 x^6}{6}-28322 x^5-2150 x^4+6432 x^3+3672 x^2+864 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

864*x + 3672*x^2 + 6432*x^3 - 2150*x^4 - 28322*x^5 - (252329*x^6)/6 - 987*x^7 + (551349*x^8)/8 + 89655*x^9 + 5
0220*x^10 + (121500*x^11)/11

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Maple [A]  time = 0.001, size = 55, normalized size = 0.8 \begin{align*}{\frac{121500\,{x}^{11}}{11}}+50220\,{x}^{10}+89655\,{x}^{9}+{\frac{551349\,{x}^{8}}{8}}-987\,{x}^{7}-{\frac{252329\,{x}^{6}}{6}}-28322\,{x}^{5}-2150\,{x}^{4}+6432\,{x}^{3}+3672\,{x}^{2}+864\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

121500/11*x^11+50220*x^10+89655*x^9+551349/8*x^8-987*x^7-252329/6*x^6-28322*x^5-2150*x^4+6432*x^3+3672*x^2+864
*x

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Maxima [A]  time = 1.03136, size = 73, normalized size = 1.09 \begin{align*} \frac{121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac{551349}{8} \, x^{8} - 987 \, x^{7} - \frac{252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

121500/11*x^11 + 50220*x^10 + 89655*x^9 + 551349/8*x^8 - 987*x^7 - 252329/6*x^6 - 28322*x^5 - 2150*x^4 + 6432*
x^3 + 3672*x^2 + 864*x

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Fricas [A]  time = 1.55853, size = 181, normalized size = 2.7 \begin{align*} \frac{121500}{11} x^{11} + 50220 x^{10} + 89655 x^{9} + \frac{551349}{8} x^{8} - 987 x^{7} - \frac{252329}{6} x^{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

121500/11*x^11 + 50220*x^10 + 89655*x^9 + 551349/8*x^8 - 987*x^7 - 252329/6*x^6 - 28322*x^5 - 2150*x^4 + 6432*
x^3 + 3672*x^2 + 864*x

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Sympy [A]  time = 0.071548, size = 58, normalized size = 0.87 \begin{align*} \frac{121500 x^{11}}{11} + 50220 x^{10} + 89655 x^{9} + \frac{551349 x^{8}}{8} - 987 x^{7} - \frac{252329 x^{6}}{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

121500*x**11/11 + 50220*x**10 + 89655*x**9 + 551349*x**8/8 - 987*x**7 - 252329*x**6/6 - 28322*x**5 - 2150*x**4
+ 6432*x**3 + 3672*x**2 + 864*x

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Giac [A]  time = 3.49947, size = 73, normalized size = 1.09 \begin{align*} \frac{121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac{551349}{8} \, x^{8} - 987 \, x^{7} - \frac{252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

121500/11*x^11 + 50220*x^10 + 89655*x^9 + 551349/8*x^8 - 987*x^7 - 252329/6*x^6 - 28322*x^5 - 2150*x^4 + 6432*
x^3 + 3672*x^2 + 864*x