3.1355 \(\int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx\)

Optimal. Leaf size=67 \[ -\frac{100 (3 x+2)^{14}}{5103}+\frac{2180 (3 x+2)^{13}}{9477}-\frac{4099 (3 x+2)^{12}}{4374}+\frac{11599 (3 x+2)^{11}}{8019}-\frac{1862 (3 x+2)^{10}}{3645}+\frac{343 (3 x+2)^9}{6561} \]

[Out]

(343*(2 + 3*x)^9)/6561 - (1862*(2 + 3*x)^10)/3645 + (11599*(2 + 3*x)^11)/8019 - (4099*(2 + 3*x)^12)/4374 + (21
80*(2 + 3*x)^13)/9477 - (100*(2 + 3*x)^14)/5103

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Rubi [A]  time = 0.0332451, 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} \[ -\frac{100 (3 x+2)^{14}}{5103}+\frac{2180 (3 x+2)^{13}}{9477}-\frac{4099 (3 x+2)^{12}}{4374}+\frac{11599 (3 x+2)^{11}}{8019}-\frac{1862 (3 x+2)^{10}}{3645}+\frac{343 (3 x+2)^9}{6561} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(343*(2 + 3*x)^9)/6561 - (1862*(2 + 3*x)^10)/3645 + (11599*(2 + 3*x)^11)/8019 - (4099*(2 + 3*x)^12)/4374 + (21
80*(2 + 3*x)^13)/9477 - (100*(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)^3 (2+3 x)^8 (3+5 x)^2 \, dx &=\int \left (\frac{343}{243} (2+3 x)^8-\frac{3724}{243} (2+3 x)^9+\frac{11599}{243} (2+3 x)^{10}-\frac{8198}{243} (2+3 x)^{11}+\frac{2180}{243} (2+3 x)^{12}-\frac{200}{243} (2+3 x)^{13}\right ) \, dx\\ &=\frac{343 (2+3 x)^9}{6561}-\frac{1862 (2+3 x)^{10}}{3645}+\frac{11599 (2+3 x)^{11}}{8019}-\frac{4099 (2+3 x)^{12}}{4374}+\frac{2180 (2+3 x)^{13}}{9477}-\frac{100 (2+3 x)^{14}}{5103}\\ \end{align*}

Mathematica [A]  time = 0.0027832, size = 87, normalized size = 1.3 \[ -\frac{656100 x^{14}}{7}-\frac{6604740 x^{13}}{13}-\frac{2220777 x^{12}}{2}-\frac{12353391 x^{11}}{11}-\frac{1073412 x^{10}}{5}+685713 x^9+679446 x^8+\frac{888528 x^7}{7}-\frac{556384 x^6}{3}-\frac{663456 x^5}{5}-15168 x^4+\frac{59392 x^3}{3}+10752 x^2+2304 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

2304*x + 10752*x^2 + (59392*x^3)/3 - 15168*x^4 - (663456*x^5)/5 - (556384*x^6)/3 + (888528*x^7)/7 + 679446*x^8
+ 685713*x^9 - (1073412*x^10)/5 - (12353391*x^11)/11 - (2220777*x^12)/2 - (6604740*x^13)/13 - (656100*x^14)/7

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Maple [A]  time = 0.001, size = 70, normalized size = 1. \begin{align*} -{\frac{656100\,{x}^{14}}{7}}-{\frac{6604740\,{x}^{13}}{13}}-{\frac{2220777\,{x}^{12}}{2}}-{\frac{12353391\,{x}^{11}}{11}}-{\frac{1073412\,{x}^{10}}{5}}+685713\,{x}^{9}+679446\,{x}^{8}+{\frac{888528\,{x}^{7}}{7}}-{\frac{556384\,{x}^{6}}{3}}-{\frac{663456\,{x}^{5}}{5}}-15168\,{x}^{4}+{\frac{59392\,{x}^{3}}{3}}+10752\,{x}^{2}+2304\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-656100/7*x^14-6604740/13*x^13-2220777/2*x^12-12353391/11*x^11-1073412/5*x^10+685713*x^9+679446*x^8+888528/7*x
^7-556384/3*x^6-663456/5*x^5-15168*x^4+59392/3*x^3+10752*x^2+2304*x

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Maxima [A]  time = 1.56074, size = 93, normalized size = 1.39 \begin{align*} -\frac{656100}{7} \, x^{14} - \frac{6604740}{13} \, x^{13} - \frac{2220777}{2} \, x^{12} - \frac{12353391}{11} \, x^{11} - \frac{1073412}{5} \, x^{10} + 685713 \, x^{9} + 679446 \, x^{8} + \frac{888528}{7} \, x^{7} - \frac{556384}{3} \, x^{6} - \frac{663456}{5} \, x^{5} - 15168 \, x^{4} + \frac{59392}{3} \, x^{3} + 10752 \, x^{2} + 2304 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-656100/7*x^14 - 6604740/13*x^13 - 2220777/2*x^12 - 12353391/11*x^11 - 1073412/5*x^10 + 685713*x^9 + 679446*x^
8 + 888528/7*x^7 - 556384/3*x^6 - 663456/5*x^5 - 15168*x^4 + 59392/3*x^3 + 10752*x^2 + 2304*x

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Fricas [A]  time = 1.21865, size = 277, normalized size = 4.13 \begin{align*} -\frac{656100}{7} x^{14} - \frac{6604740}{13} x^{13} - \frac{2220777}{2} x^{12} - \frac{12353391}{11} x^{11} - \frac{1073412}{5} x^{10} + 685713 x^{9} + 679446 x^{8} + \frac{888528}{7} x^{7} - \frac{556384}{3} x^{6} - \frac{663456}{5} x^{5} - 15168 x^{4} + \frac{59392}{3} x^{3} + 10752 x^{2} + 2304 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-656100/7*x^14 - 6604740/13*x^13 - 2220777/2*x^12 - 12353391/11*x^11 - 1073412/5*x^10 + 685713*x^9 + 679446*x^
8 + 888528/7*x^7 - 556384/3*x^6 - 663456/5*x^5 - 15168*x^4 + 59392/3*x^3 + 10752*x^2 + 2304*x

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Sympy [A]  time = 0.07727, size = 83, normalized size = 1.24 \begin{align*} - \frac{656100 x^{14}}{7} - \frac{6604740 x^{13}}{13} - \frac{2220777 x^{12}}{2} - \frac{12353391 x^{11}}{11} - \frac{1073412 x^{10}}{5} + 685713 x^{9} + 679446 x^{8} + \frac{888528 x^{7}}{7} - \frac{556384 x^{6}}{3} - \frac{663456 x^{5}}{5} - 15168 x^{4} + \frac{59392 x^{3}}{3} + 10752 x^{2} + 2304 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-656100*x**14/7 - 6604740*x**13/13 - 2220777*x**12/2 - 12353391*x**11/11 - 1073412*x**10/5 + 685713*x**9 + 679
446*x**8 + 888528*x**7/7 - 556384*x**6/3 - 663456*x**5/5 - 15168*x**4 + 59392*x**3/3 + 10752*x**2 + 2304*x

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Giac [A]  time = 2.75172, size = 93, normalized size = 1.39 \begin{align*} -\frac{656100}{7} \, x^{14} - \frac{6604740}{13} \, x^{13} - \frac{2220777}{2} \, x^{12} - \frac{12353391}{11} \, x^{11} - \frac{1073412}{5} \, x^{10} + 685713 \, x^{9} + 679446 \, x^{8} + \frac{888528}{7} \, x^{7} - \frac{556384}{3} \, x^{6} - \frac{663456}{5} \, x^{5} - 15168 \, x^{4} + \frac{59392}{3} \, x^{3} + 10752 \, x^{2} + 2304 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-656100/7*x^14 - 6604740/13*x^13 - 2220777/2*x^12 - 12353391/11*x^11 - 1073412/5*x^10 + 685713*x^9 + 679446*x^
8 + 888528/7*x^7 - 556384/3*x^6 - 663456/5*x^5 - 15168*x^4 + 59392/3*x^3 + 10752*x^2 + 2304*x