3.1276 \(\int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{50}{729} (3 x+2)^{10}-\frac{3800 (3 x+2)^9}{6561}+\frac{8285 (3 x+2)^8}{5832}-\frac{4099 (3 x+2)^7}{5103}+\frac{763 (3 x+2)^6}{4374}-\frac{49 (3 x+2)^5}{3645} \]

[Out]

(-49*(2 + 3*x)^5)/3645 + (763*(2 + 3*x)^6)/4374 - (4099*(2 + 3*x)^7)/5103 + (8285*(2 + 3*x)^8)/5832 - (3800*(2
+ 3*x)^9)/6561 + (50*(2 + 3*x)^10)/729

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Rubi [A]  time = 0.0274436, 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} \[ \frac{50}{729} (3 x+2)^{10}-\frac{3800 (3 x+2)^9}{6561}+\frac{8285 (3 x+2)^8}{5832}-\frac{4099 (3 x+2)^7}{5103}+\frac{763 (3 x+2)^6}{4374}-\frac{49 (3 x+2)^5}{3645} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3,x]

[Out]

(-49*(2 + 3*x)^5)/3645 + (763*(2 + 3*x)^6)/4374 - (4099*(2 + 3*x)^7)/5103 + (8285*(2 + 3*x)^8)/5832 - (3800*(2
+ 3*x)^9)/6561 + (50*(2 + 3*x)^10)/729

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)^4 (3+5 x)^3 \, dx &=\int \left (-\frac{49}{243} (2+3 x)^4+\frac{763}{243} (2+3 x)^5-\frac{4099}{243} (2+3 x)^6+\frac{8285}{243} (2+3 x)^7-\frac{3800}{243} (2+3 x)^8+\frac{500}{243} (2+3 x)^9\right ) \, dx\\ &=-\frac{49 (2+3 x)^5}{3645}+\frac{763 (2+3 x)^6}{4374}-\frac{4099 (2+3 x)^7}{5103}+\frac{8285 (2+3 x)^8}{5832}-\frac{3800 (2+3 x)^9}{6561}+\frac{50}{729} (2+3 x)^{10}\\ \end{align*}

Mathematica [A]  time = 0.002391, size = 57, normalized size = 0.85 \[ 4050 x^{10}+15600 x^9+\frac{175365 x^8}{8}+\frac{66873 x^7}{7}-\frac{46885 x^6}{6}-\frac{52853 x^5}{5}-2992 x^4+1704 x^3+1512 x^2+432 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x)^3,x]

[Out]

432*x + 1512*x^2 + 1704*x^3 - 2992*x^4 - (52853*x^5)/5 - (46885*x^6)/6 + (66873*x^7)/7 + (175365*x^8)/8 + 1560
0*x^9 + 4050*x^10

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Maple [A]  time = 0.001, size = 50, normalized size = 0.8 \begin{align*} 4050\,{x}^{10}+15600\,{x}^{9}+{\frac{175365\,{x}^{8}}{8}}+{\frac{66873\,{x}^{7}}{7}}-{\frac{46885\,{x}^{6}}{6}}-{\frac{52853\,{x}^{5}}{5}}-2992\,{x}^{4}+1704\,{x}^{3}+1512\,{x}^{2}+432\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x)

[Out]

4050*x^10+15600*x^9+175365/8*x^8+66873/7*x^7-46885/6*x^6-52853/5*x^5-2992*x^4+1704*x^3+1512*x^2+432*x

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Maxima [A]  time = 2.83487, size = 66, normalized size = 0.99 \begin{align*} 4050 \, x^{10} + 15600 \, x^{9} + \frac{175365}{8} \, x^{8} + \frac{66873}{7} \, x^{7} - \frac{46885}{6} \, x^{6} - \frac{52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x, algorithm="maxima")

[Out]

4050*x^10 + 15600*x^9 + 175365/8*x^8 + 66873/7*x^7 - 46885/6*x^6 - 52853/5*x^5 - 2992*x^4 + 1704*x^3 + 1512*x^
2 + 432*x

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Fricas [A]  time = 1.51789, size = 163, normalized size = 2.43 \begin{align*} 4050 x^{10} + 15600 x^{9} + \frac{175365}{8} x^{8} + \frac{66873}{7} x^{7} - \frac{46885}{6} x^{6} - \frac{52853}{5} x^{5} - 2992 x^{4} + 1704 x^{3} + 1512 x^{2} + 432 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x, algorithm="fricas")

[Out]

4050*x^10 + 15600*x^9 + 175365/8*x^8 + 66873/7*x^7 - 46885/6*x^6 - 52853/5*x^5 - 2992*x^4 + 1704*x^3 + 1512*x^
2 + 432*x

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Sympy [A]  time = 0.06788, size = 54, normalized size = 0.81 \begin{align*} 4050 x^{10} + 15600 x^{9} + \frac{175365 x^{8}}{8} + \frac{66873 x^{7}}{7} - \frac{46885 x^{6}}{6} - \frac{52853 x^{5}}{5} - 2992 x^{4} + 1704 x^{3} + 1512 x^{2} + 432 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**4*(3+5*x)**3,x)

[Out]

4050*x**10 + 15600*x**9 + 175365*x**8/8 + 66873*x**7/7 - 46885*x**6/6 - 52853*x**5/5 - 2992*x**4 + 1704*x**3 +
1512*x**2 + 432*x

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Giac [A]  time = 4.24283, size = 66, normalized size = 0.99 \begin{align*} 4050 \, x^{10} + 15600 \, x^{9} + \frac{175365}{8} \, x^{8} + \frac{66873}{7} \, x^{7} - \frac{46885}{6} \, x^{6} - \frac{52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^4*(3+5*x)^3,x, algorithm="giac")

[Out]

4050*x^10 + 15600*x^9 + 175365/8*x^8 + 66873/7*x^7 - 46885/6*x^6 - 52853/5*x^5 - 2992*x^4 + 1704*x^3 + 1512*x^
2 + 432*x