3.1274 \(\int (1-2 x)^2 (2+3 x)^6 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{125 (3 x+2)^{12}}{2187}-\frac{3800 (3 x+2)^{11}}{8019}+\frac{1657 (3 x+2)^{10}}{1458}-\frac{4099 (3 x+2)^9}{6561}+\frac{763 (3 x+2)^8}{5832}-\frac{7}{729} (3 x+2)^7 \]

[Out]

(-7*(2 + 3*x)^7)/729 + (763*(2 + 3*x)^8)/5832 - (4099*(2 + 3*x)^9)/6561 + (1657*(2 + 3*x)^10)/1458 - (3800*(2
+ 3*x)^11)/8019 + (125*(2 + 3*x)^12)/2187

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Rubi [A]  time = 0.0311978, 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} \[ \frac{125 (3 x+2)^{12}}{2187}-\frac{3800 (3 x+2)^{11}}{8019}+\frac{1657 (3 x+2)^{10}}{1458}-\frac{4099 (3 x+2)^9}{6561}+\frac{763 (3 x+2)^8}{5832}-\frac{7}{729} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^3,x]

[Out]

(-7*(2 + 3*x)^7)/729 + (763*(2 + 3*x)^8)/5832 - (4099*(2 + 3*x)^9)/6561 + (1657*(2 + 3*x)^10)/1458 - (3800*(2
+ 3*x)^11)/8019 + (125*(2 + 3*x)^12)/2187

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)^6 (3+5 x)^3 \, dx &=\int \left (-\frac{49}{243} (2+3 x)^6+\frac{763}{243} (2+3 x)^7-\frac{4099}{243} (2+3 x)^8+\frac{8285}{243} (2+3 x)^9-\frac{3800}{243} (2+3 x)^{10}+\frac{500}{243} (2+3 x)^{11}\right ) \, dx\\ &=-\frac{7}{729} (2+3 x)^7+\frac{763 (2+3 x)^8}{5832}-\frac{4099 (2+3 x)^9}{6561}+\frac{1657 (2+3 x)^{10}}{1458}-\frac{3800 (2+3 x)^{11}}{8019}+\frac{125 (2+3 x)^{12}}{2187}\\ \end{align*}

Mathematica [A]  time = 0.0024754, size = 67, normalized size = 1. \[ 30375 x^{12}+\frac{1749600 x^{11}}{11}+\frac{685017 x^{10}}{2}+363093 x^9+\frac{1081971 x^8}{8}-110115 x^7-\frac{464744 x^6}{3}-61804 x^5+10172 x^4+20208 x^3+8640 x^2+1728 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^3,x]

[Out]

1728*x + 8640*x^2 + 20208*x^3 + 10172*x^4 - 61804*x^5 - (464744*x^6)/3 - 110115*x^7 + (1081971*x^8)/8 + 363093
*x^9 + (685017*x^10)/2 + (1749600*x^11)/11 + 30375*x^12

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Maple [A]  time = 0.001, size = 60, normalized size = 0.9 \begin{align*} 30375\,{x}^{12}+{\frac{1749600\,{x}^{11}}{11}}+{\frac{685017\,{x}^{10}}{2}}+363093\,{x}^{9}+{\frac{1081971\,{x}^{8}}{8}}-110115\,{x}^{7}-{\frac{464744\,{x}^{6}}{3}}-61804\,{x}^{5}+10172\,{x}^{4}+20208\,{x}^{3}+8640\,{x}^{2}+1728\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^6*(3+5*x)^3,x)

[Out]

30375*x^12+1749600/11*x^11+685017/2*x^10+363093*x^9+1081971/8*x^8-110115*x^7-464744/3*x^6-61804*x^5+10172*x^4+
20208*x^3+8640*x^2+1728*x

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Maxima [A]  time = 1.03213, size = 80, normalized size = 1.19 \begin{align*} 30375 \, x^{12} + \frac{1749600}{11} \, x^{11} + \frac{685017}{2} \, x^{10} + 363093 \, x^{9} + \frac{1081971}{8} \, x^{8} - 110115 \, x^{7} - \frac{464744}{3} \, x^{6} - 61804 \, x^{5} + 10172 \, x^{4} + 20208 \, x^{3} + 8640 \, x^{2} + 1728 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^3,x, algorithm="maxima")

[Out]

30375*x^12 + 1749600/11*x^11 + 685017/2*x^10 + 363093*x^9 + 1081971/8*x^8 - 110115*x^7 - 464744/3*x^6 - 61804*
x^5 + 10172*x^4 + 20208*x^3 + 8640*x^2 + 1728*x

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Fricas [A]  time = 1.5488, size = 215, normalized size = 3.21 \begin{align*} 30375 x^{12} + \frac{1749600}{11} x^{11} + \frac{685017}{2} x^{10} + 363093 x^{9} + \frac{1081971}{8} x^{8} - 110115 x^{7} - \frac{464744}{3} x^{6} - 61804 x^{5} + 10172 x^{4} + 20208 x^{3} + 8640 x^{2} + 1728 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^3,x, algorithm="fricas")

[Out]

30375*x^12 + 1749600/11*x^11 + 685017/2*x^10 + 363093*x^9 + 1081971/8*x^8 - 110115*x^7 - 464744/3*x^6 - 61804*
x^5 + 10172*x^4 + 20208*x^3 + 8640*x^2 + 1728*x

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Sympy [A]  time = 0.073613, size = 65, normalized size = 0.97 \begin{align*} 30375 x^{12} + \frac{1749600 x^{11}}{11} + \frac{685017 x^{10}}{2} + 363093 x^{9} + \frac{1081971 x^{8}}{8} - 110115 x^{7} - \frac{464744 x^{6}}{3} - 61804 x^{5} + 10172 x^{4} + 20208 x^{3} + 8640 x^{2} + 1728 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**6*(3+5*x)**3,x)

[Out]

30375*x**12 + 1749600*x**11/11 + 685017*x**10/2 + 363093*x**9 + 1081971*x**8/8 - 110115*x**7 - 464744*x**6/3 -
61804*x**5 + 10172*x**4 + 20208*x**3 + 8640*x**2 + 1728*x

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Giac [A]  time = 2.3954, size = 80, normalized size = 1.19 \begin{align*} 30375 \, x^{12} + \frac{1749600}{11} \, x^{11} + \frac{685017}{2} \, x^{10} + 363093 \, x^{9} + \frac{1081971}{8} \, x^{8} - 110115 \, x^{7} - \frac{464744}{3} \, x^{6} - 61804 \, x^{5} + 10172 \, x^{4} + 20208 \, x^{3} + 8640 \, x^{2} + 1728 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^3,x, algorithm="giac")

[Out]

30375*x^12 + 1749600/11*x^11 + 685017/2*x^10 + 363093*x^9 + 1081971/8*x^8 - 110115*x^7 - 464744/3*x^6 - 61804*
x^5 + 10172*x^4 + 20208*x^3 + 8640*x^2 + 1728*x