3.1258 \(\int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx\)

Optimal. Leaf size=51 \[ \frac{675 x^8}{2}+\frac{5940 x^7}{7}+\frac{1029 x^6}{2}-\frac{1828 x^5}{5}-\frac{2045 x^4}{4}-\frac{202 x^3}{3}+138 x^2+72 x \]

[Out]

72*x + 138*x^2 - (202*x^3)/3 - (2045*x^4)/4 - (1828*x^5)/5 + (1029*x^6)/2 + (5940*x^7)/7 + (675*x^8)/2

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Rubi [A]  time = 0.0201723, antiderivative size = 51, 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} \[ \frac{675 x^8}{2}+\frac{5940 x^7}{7}+\frac{1029 x^6}{2}-\frac{1828 x^5}{5}-\frac{2045 x^4}{4}-\frac{202 x^3}{3}+138 x^2+72 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

72*x + 138*x^2 - (202*x^3)/3 - (2045*x^4)/4 - (1828*x^5)/5 + (1029*x^6)/2 + (5940*x^7)/7 + (675*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)^3 (3+5 x)^2 \, dx &=\int \left (72+276 x-202 x^2-2045 x^3-1828 x^4+3087 x^5+5940 x^6+2700 x^7\right ) \, dx\\ &=72 x+138 x^2-\frac{202 x^3}{3}-\frac{2045 x^4}{4}-\frac{1828 x^5}{5}+\frac{1029 x^6}{2}+\frac{5940 x^7}{7}+\frac{675 x^8}{2}\\ \end{align*}

Mathematica [A]  time = 0.0021384, size = 51, normalized size = 1. \[ \frac{675 x^8}{2}+\frac{5940 x^7}{7}+\frac{1029 x^6}{2}-\frac{1828 x^5}{5}-\frac{2045 x^4}{4}-\frac{202 x^3}{3}+138 x^2+72 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

72*x + 138*x^2 - (202*x^3)/3 - (2045*x^4)/4 - (1828*x^5)/5 + (1029*x^6)/2 + (5940*x^7)/7 + (675*x^8)/2

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Maple [A]  time = 0., size = 40, normalized size = 0.8 \begin{align*} 72\,x+138\,{x}^{2}-{\frac{202\,{x}^{3}}{3}}-{\frac{2045\,{x}^{4}}{4}}-{\frac{1828\,{x}^{5}}{5}}+{\frac{1029\,{x}^{6}}{2}}+{\frac{5940\,{x}^{7}}{7}}+{\frac{675\,{x}^{8}}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

72*x+138*x^2-202/3*x^3-2045/4*x^4-1828/5*x^5+1029/2*x^6+5940/7*x^7+675/2*x^8

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Maxima [A]  time = 1.10531, size = 53, normalized size = 1.04 \begin{align*} \frac{675}{2} \, x^{8} + \frac{5940}{7} \, x^{7} + \frac{1029}{2} \, x^{6} - \frac{1828}{5} \, x^{5} - \frac{2045}{4} \, x^{4} - \frac{202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

675/2*x^8 + 5940/7*x^7 + 1029/2*x^6 - 1828/5*x^5 - 2045/4*x^4 - 202/3*x^3 + 138*x^2 + 72*x

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Fricas [A]  time = 1.33593, size = 124, normalized size = 2.43 \begin{align*} \frac{675}{2} x^{8} + \frac{5940}{7} x^{7} + \frac{1029}{2} x^{6} - \frac{1828}{5} x^{5} - \frac{2045}{4} x^{4} - \frac{202}{3} x^{3} + 138 x^{2} + 72 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

675/2*x^8 + 5940/7*x^7 + 1029/2*x^6 - 1828/5*x^5 - 2045/4*x^4 - 202/3*x^3 + 138*x^2 + 72*x

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Sympy [A]  time = 0.064331, size = 48, normalized size = 0.94 \begin{align*} \frac{675 x^{8}}{2} + \frac{5940 x^{7}}{7} + \frac{1029 x^{6}}{2} - \frac{1828 x^{5}}{5} - \frac{2045 x^{4}}{4} - \frac{202 x^{3}}{3} + 138 x^{2} + 72 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

675*x**8/2 + 5940*x**7/7 + 1029*x**6/2 - 1828*x**5/5 - 2045*x**4/4 - 202*x**3/3 + 138*x**2 + 72*x

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Giac [A]  time = 2.38317, size = 53, normalized size = 1.04 \begin{align*} \frac{675}{2} \, x^{8} + \frac{5940}{7} \, x^{7} + \frac{1029}{2} \, x^{6} - \frac{1828}{5} \, x^{5} - \frac{2045}{4} \, x^{4} - \frac{202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

675/2*x^8 + 5940/7*x^7 + 1029/2*x^6 - 1828/5*x^5 - 2045/4*x^4 - 202/3*x^3 + 138*x^2 + 72*x