3.1271 \(\int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{100 (3 x+2)^{15}}{2187}-\frac{1900 (3 x+2)^{14}}{5103}+\frac{8285 (3 x+2)^{13}}{9477}-\frac{4099 (3 x+2)^{12}}{8748}+\frac{763 (3 x+2)^{11}}{8019}-\frac{49 (3 x+2)^{10}}{7290} \]

[Out]

(-49*(2 + 3*x)^10)/7290 + (763*(2 + 3*x)^11)/8019 - (4099*(2 + 3*x)^12)/8748 + (8285*(2 + 3*x)^13)/9477 - (190
0*(2 + 3*x)^14)/5103 + (100*(2 + 3*x)^15)/2187

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Rubi [A]  time = 0.0349731, 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} \[ \frac{100 (3 x+2)^{15}}{2187}-\frac{1900 (3 x+2)^{14}}{5103}+\frac{8285 (3 x+2)^{13}}{9477}-\frac{4099 (3 x+2)^{12}}{8748}+\frac{763 (3 x+2)^{11}}{8019}-\frac{49 (3 x+2)^{10}}{7290} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^9*(3 + 5*x)^3,x]

[Out]

(-49*(2 + 3*x)^10)/7290 + (763*(2 + 3*x)^11)/8019 - (4099*(2 + 3*x)^12)/8748 + (8285*(2 + 3*x)^13)/9477 - (190
0*(2 + 3*x)^14)/5103 + (100*(2 + 3*x)^15)/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)^9 (3+5 x)^3 \, dx &=\int \left (-\frac{49}{243} (2+3 x)^9+\frac{763}{243} (2+3 x)^{10}-\frac{4099}{243} (2+3 x)^{11}+\frac{8285}{243} (2+3 x)^{12}-\frac{3800}{243} (2+3 x)^{13}+\frac{500}{243} (2+3 x)^{14}\right ) \, dx\\ &=-\frac{49 (2+3 x)^{10}}{7290}+\frac{763 (2+3 x)^{11}}{8019}-\frac{4099 (2+3 x)^{12}}{8748}+\frac{8285 (2+3 x)^{13}}{9477}-\frac{1900 (2+3 x)^{14}}{5103}+\frac{100 (2+3 x)^{15}}{2187}\\ \end{align*}

Mathematica [A]  time = 0.0029466, size = 90, normalized size = 1.34 \[ 656100 x^{15}+\frac{33461100 x^{14}}{7}+\frac{200077695 x^{13}}{13}+\frac{113029263 x^{12}}{4}+\frac{342976275 x^{11}}{11}+\frac{182657511 x^{10}}{10}-180666 x^9-9703638 x^8-\frac{55216512 x^7}{7}-\frac{7363312 x^6}{3}+\frac{2732864 x^5}{5}+871936 x^4+400128 x^3+100224 x^2+13824 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^9*(3 + 5*x)^3,x]

[Out]

13824*x + 100224*x^2 + 400128*x^3 + 871936*x^4 + (2732864*x^5)/5 - (7363312*x^6)/3 - (55216512*x^7)/7 - 970363
8*x^8 - 180666*x^9 + (182657511*x^10)/10 + (342976275*x^11)/11 + (113029263*x^12)/4 + (200077695*x^13)/13 + (3
3461100*x^14)/7 + 656100*x^15

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Maple [A]  time = 0., size = 75, normalized size = 1.1 \begin{align*} 656100\,{x}^{15}+{\frac{33461100\,{x}^{14}}{7}}+{\frac{200077695\,{x}^{13}}{13}}+{\frac{113029263\,{x}^{12}}{4}}+{\frac{342976275\,{x}^{11}}{11}}+{\frac{182657511\,{x}^{10}}{10}}-180666\,{x}^{9}-9703638\,{x}^{8}-{\frac{55216512\,{x}^{7}}{7}}-{\frac{7363312\,{x}^{6}}{3}}+{\frac{2732864\,{x}^{5}}{5}}+871936\,{x}^{4}+400128\,{x}^{3}+100224\,{x}^{2}+13824\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x)

[Out]

656100*x^15+33461100/7*x^14+200077695/13*x^13+113029263/4*x^12+342976275/11*x^11+182657511/10*x^10-180666*x^9-
9703638*x^8-55216512/7*x^7-7363312/3*x^6+2732864/5*x^5+871936*x^4+400128*x^3+100224*x^2+13824*x

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Maxima [A]  time = 1.04108, size = 100, normalized size = 1.49 \begin{align*} 656100 \, x^{15} + \frac{33461100}{7} \, x^{14} + \frac{200077695}{13} \, x^{13} + \frac{113029263}{4} \, x^{12} + \frac{342976275}{11} \, x^{11} + \frac{182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac{55216512}{7} \, x^{7} - \frac{7363312}{3} \, x^{6} + \frac{2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x, algorithm="maxima")

[Out]

656100*x^15 + 33461100/7*x^14 + 200077695/13*x^13 + 113029263/4*x^12 + 342976275/11*x^11 + 182657511/10*x^10 -
180666*x^9 - 9703638*x^8 - 55216512/7*x^7 - 7363312/3*x^6 + 2732864/5*x^5 + 871936*x^4 + 400128*x^3 + 100224*
x^2 + 13824*x

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Fricas [A]  time = 1.44439, size = 317, normalized size = 4.73 \begin{align*} 656100 x^{15} + \frac{33461100}{7} x^{14} + \frac{200077695}{13} x^{13} + \frac{113029263}{4} x^{12} + \frac{342976275}{11} x^{11} + \frac{182657511}{10} x^{10} - 180666 x^{9} - 9703638 x^{8} - \frac{55216512}{7} x^{7} - \frac{7363312}{3} x^{6} + \frac{2732864}{5} x^{5} + 871936 x^{4} + 400128 x^{3} + 100224 x^{2} + 13824 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x, algorithm="fricas")

[Out]

656100*x^15 + 33461100/7*x^14 + 200077695/13*x^13 + 113029263/4*x^12 + 342976275/11*x^11 + 182657511/10*x^10 -
180666*x^9 - 9703638*x^8 - 55216512/7*x^7 - 7363312/3*x^6 + 2732864/5*x^5 + 871936*x^4 + 400128*x^3 + 100224*
x^2 + 13824*x

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Sympy [A]  time = 0.079838, size = 87, normalized size = 1.3 \begin{align*} 656100 x^{15} + \frac{33461100 x^{14}}{7} + \frac{200077695 x^{13}}{13} + \frac{113029263 x^{12}}{4} + \frac{342976275 x^{11}}{11} + \frac{182657511 x^{10}}{10} - 180666 x^{9} - 9703638 x^{8} - \frac{55216512 x^{7}}{7} - \frac{7363312 x^{6}}{3} + \frac{2732864 x^{5}}{5} + 871936 x^{4} + 400128 x^{3} + 100224 x^{2} + 13824 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**9*(3+5*x)**3,x)

[Out]

656100*x**15 + 33461100*x**14/7 + 200077695*x**13/13 + 113029263*x**12/4 + 342976275*x**11/11 + 182657511*x**1
0/10 - 180666*x**9 - 9703638*x**8 - 55216512*x**7/7 - 7363312*x**6/3 + 2732864*x**5/5 + 871936*x**4 + 400128*x
**3 + 100224*x**2 + 13824*x

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Giac [A]  time = 1.38195, size = 100, normalized size = 1.49 \begin{align*} 656100 \, x^{15} + \frac{33461100}{7} \, x^{14} + \frac{200077695}{13} \, x^{13} + \frac{113029263}{4} \, x^{12} + \frac{342976275}{11} \, x^{11} + \frac{182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac{55216512}{7} \, x^{7} - \frac{7363312}{3} \, x^{6} + \frac{2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^9*(3+5*x)^3,x, algorithm="giac")

[Out]

656100*x^15 + 33461100/7*x^14 + 200077695/13*x^13 + 113029263/4*x^12 + 342976275/11*x^11 + 182657511/10*x^10 -
180666*x^9 - 9703638*x^8 - 55216512/7*x^7 - 7363312/3*x^6 + 2732864/5*x^5 + 871936*x^4 + 400128*x^3 + 100224*
x^2 + 13824*x