3.1361 \(\int (1-2 x)^3 (2+3 x)^2 (3+5 x)^2 \, dx\)

Optimal. Leaf size=47 \[ -225 x^8-\frac{1860 x^7}{7}+\frac{581 x^6}{3}+\frac{1473 x^5}{5}-57 x^4-\frac{395 x^3}{3}+6 x^2+36 x \]

[Out]

36*x + 6*x^2 - (395*x^3)/3 - 57*x^4 + (1473*x^5)/5 + (581*x^6)/3 - (1860*x^7)/7 - 225*x^8

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Rubi [A]  time = 0.0213267, antiderivative size = 47, 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} \[ -225 x^8-\frac{1860 x^7}{7}+\frac{581 x^6}{3}+\frac{1473 x^5}{5}-57 x^4-\frac{395 x^3}{3}+6 x^2+36 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 6*x^2 - (395*x^3)/3 - 57*x^4 + (1473*x^5)/5 + (581*x^6)/3 - (1860*x^7)/7 - 225*x^8

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)^2 \, dx &=\int \left (36+12 x-395 x^2-228 x^3+1473 x^4+1162 x^5-1860 x^6-1800 x^7\right ) \, dx\\ &=36 x+6 x^2-\frac{395 x^3}{3}-57 x^4+\frac{1473 x^5}{5}+\frac{581 x^6}{3}-\frac{1860 x^7}{7}-225 x^8\\ \end{align*}

Mathematica [A]  time = 0.0013372, size = 47, normalized size = 1. \[ -225 x^8-\frac{1860 x^7}{7}+\frac{581 x^6}{3}+\frac{1473 x^5}{5}-57 x^4-\frac{395 x^3}{3}+6 x^2+36 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

36*x + 6*x^2 - (395*x^3)/3 - 57*x^4 + (1473*x^5)/5 + (581*x^6)/3 - (1860*x^7)/7 - 225*x^8

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Maple [A]  time = 0., size = 40, normalized size = 0.9 \begin{align*} 36\,x+6\,{x}^{2}-{\frac{395\,{x}^{3}}{3}}-57\,{x}^{4}+{\frac{1473\,{x}^{5}}{5}}+{\frac{581\,{x}^{6}}{3}}-{\frac{1860\,{x}^{7}}{7}}-225\,{x}^{8} \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)^2,x)

[Out]

36*x+6*x^2-395/3*x^3-57*x^4+1473/5*x^5+581/3*x^6-1860/7*x^7-225*x^8

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Maxima [A]  time = 1.01445, size = 53, normalized size = 1.13 \begin{align*} -225 \, x^{8} - \frac{1860}{7} \, x^{7} + \frac{581}{3} \, x^{6} + \frac{1473}{5} \, x^{5} - 57 \, x^{4} - \frac{395}{3} \, x^{3} + 6 \, x^{2} + 36 \, 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)^2,x, algorithm="maxima")

[Out]

-225*x^8 - 1860/7*x^7 + 581/3*x^6 + 1473/5*x^5 - 57*x^4 - 395/3*x^3 + 6*x^2 + 36*x

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Fricas [A]  time = 1.09715, size = 113, normalized size = 2.4 \begin{align*} -225 x^{8} - \frac{1860}{7} x^{7} + \frac{581}{3} x^{6} + \frac{1473}{5} x^{5} - 57 x^{4} - \frac{395}{3} x^{3} + 6 x^{2} + 36 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)^2,x, algorithm="fricas")

[Out]

-225*x^8 - 1860/7*x^7 + 581/3*x^6 + 1473/5*x^5 - 57*x^4 - 395/3*x^3 + 6*x^2 + 36*x

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Sympy [A]  time = 0.06397, size = 44, normalized size = 0.94 \begin{align*} - 225 x^{8} - \frac{1860 x^{7}}{7} + \frac{581 x^{6}}{3} + \frac{1473 x^{5}}{5} - 57 x^{4} - \frac{395 x^{3}}{3} + 6 x^{2} + 36 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)**2,x)

[Out]

-225*x**8 - 1860*x**7/7 + 581*x**6/3 + 1473*x**5/5 - 57*x**4 - 395*x**3/3 + 6*x**2 + 36*x

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Giac [A]  time = 2.66295, size = 53, normalized size = 1.13 \begin{align*} -225 \, x^{8} - \frac{1860}{7} \, x^{7} + \frac{581}{3} \, x^{6} + \frac{1473}{5} \, x^{5} - 57 \, x^{4} - \frac{395}{3} \, x^{3} + 6 \, x^{2} + 36 \, 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)^2,x, algorithm="giac")

[Out]

-225*x^8 - 1860/7*x^7 + 581/3*x^6 + 1473/5*x^5 - 57*x^4 - 395/3*x^3 + 6*x^2 + 36*x