3.1272 \(\int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{250 (3 x+2)^{14}}{5103}-\frac{3800 (3 x+2)^{13}}{9477}+\frac{8285 (3 x+2)^{12}}{8748}-\frac{4099 (3 x+2)^{11}}{8019}+\frac{763 (3 x+2)^{10}}{7290}-\frac{49 (3 x+2)^9}{6561} \]

[Out]

(-49*(2 + 3*x)^9)/6561 + (763*(2 + 3*x)^10)/7290 - (4099*(2 + 3*x)^11)/8019 + (8285*(2 + 3*x)^12)/8748 - (3800
*(2 + 3*x)^13)/9477 + (250*(2 + 3*x)^14)/5103

________________________________________________________________________________________

Rubi [A]  time = 0.0355555, 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} \[ \frac{250 (3 x+2)^{14}}{5103}-\frac{3800 (3 x+2)^{13}}{9477}+\frac{8285 (3 x+2)^{12}}{8748}-\frac{4099 (3 x+2)^{11}}{8019}+\frac{763 (3 x+2)^{10}}{7290}-\frac{49 (3 x+2)^9}{6561} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^3,x]

[Out]

(-49*(2 + 3*x)^9)/6561 + (763*(2 + 3*x)^10)/7290 - (4099*(2 + 3*x)^11)/8019 + (8285*(2 + 3*x)^12)/8748 - (3800
*(2 + 3*x)^13)/9477 + (250*(2 + 3*x)^14)/5103

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)^8 (3+5 x)^3 \, dx &=\int \left (-\frac{49}{243} (2+3 x)^8+\frac{763}{243} (2+3 x)^9-\frac{4099}{243} (2+3 x)^{10}+\frac{8285}{243} (2+3 x)^{11}-\frac{3800}{243} (2+3 x)^{12}+\frac{500}{243} (2+3 x)^{13}\right ) \, dx\\ &=-\frac{49 (2+3 x)^9}{6561}+\frac{763 (2+3 x)^{10}}{7290}-\frac{4099 (2+3 x)^{11}}{8019}+\frac{8285 (2+3 x)^{12}}{8748}-\frac{3800 (2+3 x)^{13}}{9477}+\frac{250 (2+3 x)^{14}}{5103}\\ \end{align*}

Mathematica [A]  time = 0.0025085, size = 85, normalized size = 1.27 \[ \frac{1640250 x^{14}}{7}+\frac{20120400 x^{13}}{13}+\frac{17759655 x^{12}}{4}+\frac{77509953 x^{11}}{11}+\frac{62652123 x^{10}}{10}+2124195 x^9-1660896 x^8-\frac{17018256 x^7}{7}-\frac{3530000 x^6}{3}-\frac{202208 x^5}{5}+261440 x^4+155136 x^3+44928 x^2+6912 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^3,x]

[Out]

6912*x + 44928*x^2 + 155136*x^3 + 261440*x^4 - (202208*x^5)/5 - (3530000*x^6)/3 - (17018256*x^7)/7 - 1660896*x
^8 + 2124195*x^9 + (62652123*x^10)/10 + (77509953*x^11)/11 + (17759655*x^12)/4 + (20120400*x^13)/13 + (1640250
*x^14)/7

________________________________________________________________________________________

Maple [A]  time = 0.001, size = 70, normalized size = 1. \begin{align*}{\frac{1640250\,{x}^{14}}{7}}+{\frac{20120400\,{x}^{13}}{13}}+{\frac{17759655\,{x}^{12}}{4}}+{\frac{77509953\,{x}^{11}}{11}}+{\frac{62652123\,{x}^{10}}{10}}+2124195\,{x}^{9}-1660896\,{x}^{8}-{\frac{17018256\,{x}^{7}}{7}}-{\frac{3530000\,{x}^{6}}{3}}-{\frac{202208\,{x}^{5}}{5}}+261440\,{x}^{4}+155136\,{x}^{3}+44928\,{x}^{2}+6912\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^8*(3+5*x)^3,x)

[Out]

1640250/7*x^14+20120400/13*x^13+17759655/4*x^12+77509953/11*x^11+62652123/10*x^10+2124195*x^9-1660896*x^8-1701
8256/7*x^7-3530000/3*x^6-202208/5*x^5+261440*x^4+155136*x^3+44928*x^2+6912*x

________________________________________________________________________________________

Maxima [A]  time = 2.25272, size = 93, normalized size = 1.39 \begin{align*} \frac{1640250}{7} \, x^{14} + \frac{20120400}{13} \, x^{13} + \frac{17759655}{4} \, x^{12} + \frac{77509953}{11} \, x^{11} + \frac{62652123}{10} \, x^{10} + 2124195 \, x^{9} - 1660896 \, x^{8} - \frac{17018256}{7} \, x^{7} - \frac{3530000}{3} \, x^{6} - \frac{202208}{5} \, x^{5} + 261440 \, x^{4} + 155136 \, x^{3} + 44928 \, x^{2} + 6912 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x)^3,x, algorithm="maxima")

[Out]

1640250/7*x^14 + 20120400/13*x^13 + 17759655/4*x^12 + 77509953/11*x^11 + 62652123/10*x^10 + 2124195*x^9 - 1660
896*x^8 - 17018256/7*x^7 - 3530000/3*x^6 - 202208/5*x^5 + 261440*x^4 + 155136*x^3 + 44928*x^2 + 6912*x

________________________________________________________________________________________

Fricas [A]  time = 1.49451, size = 289, normalized size = 4.31 \begin{align*} \frac{1640250}{7} x^{14} + \frac{20120400}{13} x^{13} + \frac{17759655}{4} x^{12} + \frac{77509953}{11} x^{11} + \frac{62652123}{10} x^{10} + 2124195 x^{9} - 1660896 x^{8} - \frac{17018256}{7} x^{7} - \frac{3530000}{3} x^{6} - \frac{202208}{5} x^{5} + 261440 x^{4} + 155136 x^{3} + 44928 x^{2} + 6912 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x)^3,x, algorithm="fricas")

[Out]

1640250/7*x^14 + 20120400/13*x^13 + 17759655/4*x^12 + 77509953/11*x^11 + 62652123/10*x^10 + 2124195*x^9 - 1660
896*x^8 - 17018256/7*x^7 - 3530000/3*x^6 - 202208/5*x^5 + 261440*x^4 + 155136*x^3 + 44928*x^2 + 6912*x

________________________________________________________________________________________

Sympy [A]  time = 0.077867, size = 82, normalized size = 1.22 \begin{align*} \frac{1640250 x^{14}}{7} + \frac{20120400 x^{13}}{13} + \frac{17759655 x^{12}}{4} + \frac{77509953 x^{11}}{11} + \frac{62652123 x^{10}}{10} + 2124195 x^{9} - 1660896 x^{8} - \frac{17018256 x^{7}}{7} - \frac{3530000 x^{6}}{3} - \frac{202208 x^{5}}{5} + 261440 x^{4} + 155136 x^{3} + 44928 x^{2} + 6912 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**8*(3+5*x)**3,x)

[Out]

1640250*x**14/7 + 20120400*x**13/13 + 17759655*x**12/4 + 77509953*x**11/11 + 62652123*x**10/10 + 2124195*x**9
- 1660896*x**8 - 17018256*x**7/7 - 3530000*x**6/3 - 202208*x**5/5 + 261440*x**4 + 155136*x**3 + 44928*x**2 + 6
912*x

________________________________________________________________________________________

Giac [A]  time = 1.51176, size = 93, normalized size = 1.39 \begin{align*} \frac{1640250}{7} \, x^{14} + \frac{20120400}{13} \, x^{13} + \frac{17759655}{4} \, x^{12} + \frac{77509953}{11} \, x^{11} + \frac{62652123}{10} \, x^{10} + 2124195 \, x^{9} - 1660896 \, x^{8} - \frac{17018256}{7} \, x^{7} - \frac{3530000}{3} \, x^{6} - \frac{202208}{5} \, x^{5} + 261440 \, x^{4} + 155136 \, x^{3} + 44928 \, x^{2} + 6912 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x)^3,x, algorithm="giac")

[Out]

1640250/7*x^14 + 20120400/13*x^13 + 17759655/4*x^12 + 77509953/11*x^11 + 62652123/10*x^10 + 2124195*x^9 - 1660
896*x^8 - 17018256/7*x^7 - 3530000/3*x^6 - 202208/5*x^5 + 261440*x^4 + 155136*x^3 + 44928*x^2 + 6912*x