3.1278 \(\int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx\)

Optimal. Leaf size=49 \[ \frac{1125 x^8}{2}+\frac{9600 x^7}{7}+\frac{4685 x^6}{6}-\frac{3083 x^5}{5}-\frac{3181 x^4}{4}-87 x^3+216 x^2+108 x \]

[Out]

108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2

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Rubi [A]  time = 0.0196127, antiderivative size = 49, 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} \[ \frac{1125 x^8}{2}+\frac{9600 x^7}{7}+\frac{4685 x^6}{6}-\frac{3083 x^5}{5}-\frac{3181 x^4}{4}-87 x^3+216 x^2+108 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2

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)^2 (3+5 x)^3 \, dx &=\int \left (108+432 x-261 x^2-3181 x^3-3083 x^4+4685 x^5+9600 x^6+4500 x^7\right ) \, dx\\ &=108 x+216 x^2-87 x^3-\frac{3181 x^4}{4}-\frac{3083 x^5}{5}+\frac{4685 x^6}{6}+\frac{9600 x^7}{7}+\frac{1125 x^8}{2}\\ \end{align*}

Mathematica [A]  time = 0.0023153, size = 49, normalized size = 1. \[ \frac{1125 x^8}{2}+\frac{9600 x^7}{7}+\frac{4685 x^6}{6}-\frac{3083 x^5}{5}-\frac{3181 x^4}{4}-87 x^3+216 x^2+108 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^7)/7 + (1125*x^8)/2

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Maple [A]  time = 0.001, size = 40, normalized size = 0.8 \begin{align*} 108\,x+216\,{x}^{2}-87\,{x}^{3}-{\frac{3181\,{x}^{4}}{4}}-{\frac{3083\,{x}^{5}}{5}}+{\frac{4685\,{x}^{6}}{6}}+{\frac{9600\,{x}^{7}}{7}}+{\frac{1125\,{x}^{8}}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

108*x+216*x^2-87*x^3-3181/4*x^4-3083/5*x^5+4685/6*x^6+9600/7*x^7+1125/2*x^8

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Maxima [A]  time = 1.16172, size = 53, normalized size = 1.08 \begin{align*} \frac{1125}{2} \, x^{8} + \frac{9600}{7} \, x^{7} + \frac{4685}{6} \, x^{6} - \frac{3083}{5} \, x^{5} - \frac{3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^2 + 108*x

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Fricas [A]  time = 1.54467, size = 123, normalized size = 2.51 \begin{align*} \frac{1125}{2} x^{8} + \frac{9600}{7} x^{7} + \frac{4685}{6} x^{6} - \frac{3083}{5} x^{5} - \frac{3181}{4} x^{4} - 87 x^{3} + 216 x^{2} + 108 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^2 + 108*x

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Sympy [A]  time = 0.063659, size = 46, normalized size = 0.94 \begin{align*} \frac{1125 x^{8}}{2} + \frac{9600 x^{7}}{7} + \frac{4685 x^{6}}{6} - \frac{3083 x^{5}}{5} - \frac{3181 x^{4}}{4} - 87 x^{3} + 216 x^{2} + 108 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1125*x**8/2 + 9600*x**7/7 + 4685*x**6/6 - 3083*x**5/5 - 3181*x**4/4 - 87*x**3 + 216*x**2 + 108*x

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Giac [A]  time = 2.41522, size = 53, normalized size = 1.08 \begin{align*} \frac{1125}{2} \, x^{8} + \frac{9600}{7} \, x^{7} + \frac{4685}{6} \, x^{6} - \frac{3083}{5} \, x^{5} - \frac{3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^2 + 108*x