3.1273 \(\int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{500 (3 x+2)^{13}}{9477}-\frac{950 (3 x+2)^{12}}{2187}+\frac{8285 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{7290}+\frac{763 (3 x+2)^9}{6561}-\frac{49 (3 x+2)^8}{5832} \]

[Out]

(-49*(2 + 3*x)^8)/5832 + (763*(2 + 3*x)^9)/6561 - (4099*(2 + 3*x)^10)/7290 + (8285*(2 + 3*x)^11)/8019 - (950*(
2 + 3*x)^12)/2187 + (500*(2 + 3*x)^13)/9477

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Rubi [A]  time = 0.0324613, 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} \[ \frac{500 (3 x+2)^{13}}{9477}-\frac{950 (3 x+2)^{12}}{2187}+\frac{8285 (3 x+2)^{11}}{8019}-\frac{4099 (3 x+2)^{10}}{7290}+\frac{763 (3 x+2)^9}{6561}-\frac{49 (3 x+2)^8}{5832} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3,x]

[Out]

(-49*(2 + 3*x)^8)/5832 + (763*(2 + 3*x)^9)/6561 - (4099*(2 + 3*x)^10)/7290 + (8285*(2 + 3*x)^11)/8019 - (950*(
2 + 3*x)^12)/2187 + (500*(2 + 3*x)^13)/9477

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)^7 (3+5 x)^3 \, dx &=\int \left (-\frac{49}{243} (2+3 x)^7+\frac{763}{243} (2+3 x)^8-\frac{4099}{243} (2+3 x)^9+\frac{8285}{243} (2+3 x)^{10}-\frac{3800}{243} (2+3 x)^{11}+\frac{500}{243} (2+3 x)^{12}\right ) \, dx\\ &=-\frac{49 (2+3 x)^8}{5832}+\frac{763 (2+3 x)^9}{6561}-\frac{4099 (2+3 x)^{10}}{7290}+\frac{8285 (2+3 x)^{11}}{8019}-\frac{950 (2+3 x)^{12}}{2187}+\frac{500 (2+3 x)^{13}}{9477}\\ \end{align*}

Mathematica [A]  time = 0.0025098, size = 76, normalized size = 1.13 \[ \frac{1093500 x^{13}}{13}+498150 x^{12}+\frac{13774455 x^{11}}{11}+\frac{16653681 x^{10}}{10}+1086843 x^9-\frac{148473 x^8}{8}-618582 x^7-\frac{1393018 x^6}{3}-\frac{495976 x^5}{5}+65812 x^4+57696 x^3+19872 x^2+3456 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^7*(3 + 5*x)^3,x]

[Out]

3456*x + 19872*x^2 + 57696*x^3 + 65812*x^4 - (495976*x^5)/5 - (1393018*x^6)/3 - 618582*x^7 - (148473*x^8)/8 +
1086843*x^9 + (16653681*x^10)/10 + (13774455*x^11)/11 + 498150*x^12 + (1093500*x^13)/13

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Maple [A]  time = 0.001, size = 65, normalized size = 1. \begin{align*}{\frac{1093500\,{x}^{13}}{13}}+498150\,{x}^{12}+{\frac{13774455\,{x}^{11}}{11}}+{\frac{16653681\,{x}^{10}}{10}}+1086843\,{x}^{9}-{\frac{148473\,{x}^{8}}{8}}-618582\,{x}^{7}-{\frac{1393018\,{x}^{6}}{3}}-{\frac{495976\,{x}^{5}}{5}}+65812\,{x}^{4}+57696\,{x}^{3}+19872\,{x}^{2}+3456\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x)

[Out]

1093500/13*x^13+498150*x^12+13774455/11*x^11+16653681/10*x^10+1086843*x^9-148473/8*x^8-618582*x^7-1393018/3*x^
6-495976/5*x^5+65812*x^4+57696*x^3+19872*x^2+3456*x

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Maxima [A]  time = 1.06646, size = 86, normalized size = 1.28 \begin{align*} \frac{1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac{13774455}{11} \, x^{11} + \frac{16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac{148473}{8} \, x^{8} - 618582 \, x^{7} - \frac{1393018}{3} \, x^{6} - \frac{495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x, algorithm="maxima")

[Out]

1093500/13*x^13 + 498150*x^12 + 13774455/11*x^11 + 16653681/10*x^10 + 1086843*x^9 - 148473/8*x^8 - 618582*x^7
- 1393018/3*x^6 - 495976/5*x^5 + 65812*x^4 + 57696*x^3 + 19872*x^2 + 3456*x

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Fricas [A]  time = 1.47861, size = 252, normalized size = 3.76 \begin{align*} \frac{1093500}{13} x^{13} + 498150 x^{12} + \frac{13774455}{11} x^{11} + \frac{16653681}{10} x^{10} + 1086843 x^{9} - \frac{148473}{8} x^{8} - 618582 x^{7} - \frac{1393018}{3} x^{6} - \frac{495976}{5} x^{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x, algorithm="fricas")

[Out]

1093500/13*x^13 + 498150*x^12 + 13774455/11*x^11 + 16653681/10*x^10 + 1086843*x^9 - 148473/8*x^8 - 618582*x^7
- 1393018/3*x^6 - 495976/5*x^5 + 65812*x^4 + 57696*x^3 + 19872*x^2 + 3456*x

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Sympy [A]  time = 0.074877, size = 73, normalized size = 1.09 \begin{align*} \frac{1093500 x^{13}}{13} + 498150 x^{12} + \frac{13774455 x^{11}}{11} + \frac{16653681 x^{10}}{10} + 1086843 x^{9} - \frac{148473 x^{8}}{8} - 618582 x^{7} - \frac{1393018 x^{6}}{3} - \frac{495976 x^{5}}{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**7*(3+5*x)**3,x)

[Out]

1093500*x**13/13 + 498150*x**12 + 13774455*x**11/11 + 16653681*x**10/10 + 1086843*x**9 - 148473*x**8/8 - 61858
2*x**7 - 1393018*x**6/3 - 495976*x**5/5 + 65812*x**4 + 57696*x**3 + 19872*x**2 + 3456*x

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Giac [A]  time = 1.88717, size = 86, normalized size = 1.28 \begin{align*} \frac{1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac{13774455}{11} \, x^{11} + \frac{16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac{148473}{8} \, x^{8} - 618582 \, x^{7} - \frac{1393018}{3} \, x^{6} - \frac{495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^7*(3+5*x)^3,x, algorithm="giac")

[Out]

1093500/13*x^13 + 498150*x^12 + 13774455/11*x^11 + 16653681/10*x^10 + 1086843*x^9 - 148473/8*x^8 - 618582*x^7
- 1393018/3*x^6 - 495976/5*x^5 + 65812*x^4 + 57696*x^3 + 19872*x^2 + 3456*x