3.1377 \(\int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx\)

Optimal. Leaf size=54 \[ -1000 x^9-\frac{3675 x^8}{2}+\frac{230 x^7}{7}+\frac{3617 x^6}{2}+\frac{3279 x^5}{5}-\frac{2659 x^4}{4}-375 x^3+108 x^2+108 x \]

[Out]

108*x + 108*x^2 - 375*x^3 - (2659*x^4)/4 + (3279*x^5)/5 + (3617*x^6)/2 + (230*x^7)/7 - (3675*x^8)/2 - 1000*x^9

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Rubi [A]  time = 0.0225201, antiderivative size = 54, 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} \[ -1000 x^9-\frac{3675 x^8}{2}+\frac{230 x^7}{7}+\frac{3617 x^6}{2}+\frac{3279 x^5}{5}-\frac{2659 x^4}{4}-375 x^3+108 x^2+108 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

108*x + 108*x^2 - 375*x^3 - (2659*x^4)/4 + (3279*x^5)/5 + (3617*x^6)/2 + (230*x^7)/7 - (3675*x^8)/2 - 1000*x^9

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)^2 (3+5 x)^3 \, dx &=\int \left (108+216 x-1125 x^2-2659 x^3+3279 x^4+10851 x^5+230 x^6-14700 x^7-9000 x^8\right ) \, dx\\ &=108 x+108 x^2-375 x^3-\frac{2659 x^4}{4}+\frac{3279 x^5}{5}+\frac{3617 x^6}{2}+\frac{230 x^7}{7}-\frac{3675 x^8}{2}-1000 x^9\\ \end{align*}

Mathematica [A]  time = 0.0022065, size = 54, normalized size = 1. \[ -1000 x^9-\frac{3675 x^8}{2}+\frac{230 x^7}{7}+\frac{3617 x^6}{2}+\frac{3279 x^5}{5}-\frac{2659 x^4}{4}-375 x^3+108 x^2+108 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

108*x + 108*x^2 - 375*x^3 - (2659*x^4)/4 + (3279*x^5)/5 + (3617*x^6)/2 + (230*x^7)/7 - (3675*x^8)/2 - 1000*x^9

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Maple [A]  time = 0., size = 45, normalized size = 0.8 \begin{align*} 108\,x+108\,{x}^{2}-375\,{x}^{3}-{\frac{2659\,{x}^{4}}{4}}+{\frac{3279\,{x}^{5}}{5}}+{\frac{3617\,{x}^{6}}{2}}+{\frac{230\,{x}^{7}}{7}}-{\frac{3675\,{x}^{8}}{2}}-1000\,{x}^{9} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

108*x+108*x^2-375*x^3-2659/4*x^4+3279/5*x^5+3617/2*x^6+230/7*x^7-3675/2*x^8-1000*x^9

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Maxima [A]  time = 1.21777, size = 59, normalized size = 1.09 \begin{align*} -1000 \, x^{9} - \frac{3675}{2} \, x^{8} + \frac{230}{7} \, x^{7} + \frac{3617}{2} \, x^{6} + \frac{3279}{5} \, x^{5} - \frac{2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1000*x^9 - 3675/2*x^8 + 230/7*x^7 + 3617/2*x^6 + 3279/5*x^5 - 2659/4*x^4 - 375*x^3 + 108*x^2 + 108*x

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Fricas [A]  time = 1.04753, size = 139, normalized size = 2.57 \begin{align*} -1000 x^{9} - \frac{3675}{2} x^{8} + \frac{230}{7} x^{7} + \frac{3617}{2} x^{6} + \frac{3279}{5} x^{5} - \frac{2659}{4} x^{4} - 375 x^{3} + 108 x^{2} + 108 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1000*x^9 - 3675/2*x^8 + 230/7*x^7 + 3617/2*x^6 + 3279/5*x^5 - 2659/4*x^4 - 375*x^3 + 108*x^2 + 108*x

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Sympy [A]  time = 0.06642, size = 51, normalized size = 0.94 \begin{align*} - 1000 x^{9} - \frac{3675 x^{8}}{2} + \frac{230 x^{7}}{7} + \frac{3617 x^{6}}{2} + \frac{3279 x^{5}}{5} - \frac{2659 x^{4}}{4} - 375 x^{3} + 108 x^{2} + 108 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1000*x**9 - 3675*x**8/2 + 230*x**7/7 + 3617*x**6/2 + 3279*x**5/5 - 2659*x**4/4 - 375*x**3 + 108*x**2 + 108*x

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Giac [A]  time = 2.8249, size = 59, normalized size = 1.09 \begin{align*} -1000 \, x^{9} - \frac{3675}{2} \, x^{8} + \frac{230}{7} \, x^{7} + \frac{3617}{2} \, x^{6} + \frac{3279}{5} \, x^{5} - \frac{2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1000*x^9 - 3675/2*x^8 + 230/7*x^7 + 3617/2*x^6 + 3279/5*x^5 - 2659/4*x^4 - 375*x^3 + 108*x^2 + 108*x