3.1376 \(\int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx\)

Optimal. Leaf size=59 \[ -2700 x^{10}-6900 x^9-\frac{14355 x^8}{4}+\frac{33013 x^7}{7}+\frac{10513 x^6}{2}-\frac{1419 x^5}{5}-\frac{8693 x^4}{4}-534 x^3+378 x^2+216 x \]

[Out]

216*x + 378*x^2 - 534*x^3 - (8693*x^4)/4 - (1419*x^5)/5 + (10513*x^6)/2 + (33013*x^7)/7 - (14355*x^8)/4 - 6900
*x^9 - 2700*x^10

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Rubi [A]  time = 0.0249694, antiderivative size = 59, 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} \[ -2700 x^{10}-6900 x^9-\frac{14355 x^8}{4}+\frac{33013 x^7}{7}+\frac{10513 x^6}{2}-\frac{1419 x^5}{5}-\frac{8693 x^4}{4}-534 x^3+378 x^2+216 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 378*x^2 - 534*x^3 - (8693*x^4)/4 - (1419*x^5)/5 + (10513*x^6)/2 + (33013*x^7)/7 - (14355*x^8)/4 - 6900
*x^9 - 2700*x^10

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)^3 (3+5 x)^3 \, dx &=\int \left (216+756 x-1602 x^2-8693 x^3-1419 x^4+31539 x^5+33013 x^6-28710 x^7-62100 x^8-27000 x^9\right ) \, dx\\ &=216 x+378 x^2-534 x^3-\frac{8693 x^4}{4}-\frac{1419 x^5}{5}+\frac{10513 x^6}{2}+\frac{33013 x^7}{7}-\frac{14355 x^8}{4}-6900 x^9-2700 x^{10}\\ \end{align*}

Mathematica [A]  time = 0.0024707, size = 59, normalized size = 1. \[ -2700 x^{10}-6900 x^9-\frac{14355 x^8}{4}+\frac{33013 x^7}{7}+\frac{10513 x^6}{2}-\frac{1419 x^5}{5}-\frac{8693 x^4}{4}-534 x^3+378 x^2+216 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

216*x + 378*x^2 - 534*x^3 - (8693*x^4)/4 - (1419*x^5)/5 + (10513*x^6)/2 + (33013*x^7)/7 - (14355*x^8)/4 - 6900
*x^9 - 2700*x^10

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Maple [A]  time = 0.002, size = 50, normalized size = 0.9 \begin{align*} 216\,x+378\,{x}^{2}-534\,{x}^{3}-{\frac{8693\,{x}^{4}}{4}}-{\frac{1419\,{x}^{5}}{5}}+{\frac{10513\,{x}^{6}}{2}}+{\frac{33013\,{x}^{7}}{7}}-{\frac{14355\,{x}^{8}}{4}}-6900\,{x}^{9}-2700\,{x}^{10} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

216*x+378*x^2-534*x^3-8693/4*x^4-1419/5*x^5+10513/2*x^6+33013/7*x^7-14355/4*x^8-6900*x^9-2700*x^10

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Maxima [A]  time = 1.04065, size = 66, normalized size = 1.12 \begin{align*} -2700 \, x^{10} - 6900 \, x^{9} - \frac{14355}{4} \, x^{8} + \frac{33013}{7} \, x^{7} + \frac{10513}{2} \, x^{6} - \frac{1419}{5} \, x^{5} - \frac{8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2700*x^10 - 6900*x^9 - 14355/4*x^8 + 33013/7*x^7 + 10513/2*x^6 - 1419/5*x^5 - 8693/4*x^4 - 534*x^3 + 378*x^2
+ 216*x

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Fricas [A]  time = 1.03422, size = 161, normalized size = 2.73 \begin{align*} -2700 x^{10} - 6900 x^{9} - \frac{14355}{4} x^{8} + \frac{33013}{7} x^{7} + \frac{10513}{2} x^{6} - \frac{1419}{5} x^{5} - \frac{8693}{4} x^{4} - 534 x^{3} + 378 x^{2} + 216 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2700*x^10 - 6900*x^9 - 14355/4*x^8 + 33013/7*x^7 + 10513/2*x^6 - 1419/5*x^5 - 8693/4*x^4 - 534*x^3 + 378*x^2
+ 216*x

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Sympy [A]  time = 0.066971, size = 56, normalized size = 0.95 \begin{align*} - 2700 x^{10} - 6900 x^{9} - \frac{14355 x^{8}}{4} + \frac{33013 x^{7}}{7} + \frac{10513 x^{6}}{2} - \frac{1419 x^{5}}{5} - \frac{8693 x^{4}}{4} - 534 x^{3} + 378 x^{2} + 216 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2700*x**10 - 6900*x**9 - 14355*x**8/4 + 33013*x**7/7 + 10513*x**6/2 - 1419*x**5/5 - 8693*x**4/4 - 534*x**3 +
378*x**2 + 216*x

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Giac [A]  time = 2.55003, size = 66, normalized size = 1.12 \begin{align*} -2700 \, x^{10} - 6900 \, x^{9} - \frac{14355}{4} \, x^{8} + \frac{33013}{7} \, x^{7} + \frac{10513}{2} \, x^{6} - \frac{1419}{5} \, x^{5} - \frac{8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-2700*x^10 - 6900*x^9 - 14355/4*x^8 + 33013/7*x^7 + 10513/2*x^6 - 1419/5*x^5 - 8693/4*x^4 - 534*x^3 + 378*x^2
+ 216*x