3.1359 \(\int (1-2 x)^3 (2+3 x)^4 (3+5 x)^2 \, dx\)

Optimal. Leaf size=67 \[ -\frac{20}{729} (3 x+2)^{10}+\frac{2180 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{2916}+\frac{1657}{729} (3 x+2)^7-\frac{1862 (3 x+2)^6}{2187}+\frac{343 (3 x+2)^5}{3645} \]

[Out]

(343*(2 + 3*x)^5)/3645 - (1862*(2 + 3*x)^6)/2187 + (1657*(2 + 3*x)^7)/729 - (4099*(2 + 3*x)^8)/2916 + (2180*(2
+ 3*x)^9)/6561 - (20*(2 + 3*x)^10)/729

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Rubi [A]  time = 0.028602, antiderivative size = 67, 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} \[ -\frac{20}{729} (3 x+2)^{10}+\frac{2180 (3 x+2)^9}{6561}-\frac{4099 (3 x+2)^8}{2916}+\frac{1657}{729} (3 x+2)^7-\frac{1862 (3 x+2)^6}{2187}+\frac{343 (3 x+2)^5}{3645} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

(343*(2 + 3*x)^5)/3645 - (1862*(2 + 3*x)^6)/2187 + (1657*(2 + 3*x)^7)/729 - (4099*(2 + 3*x)^8)/2916 + (2180*(2
+ 3*x)^9)/6561 - (20*(2 + 3*x)^10)/729

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)^4 (3+5 x)^2 \, dx &=\int \left (\frac{343}{243} (2+3 x)^4-\frac{3724}{243} (2+3 x)^5+\frac{11599}{243} (2+3 x)^6-\frac{8198}{243} (2+3 x)^7+\frac{2180}{243} (2+3 x)^8-\frac{200}{243} (2+3 x)^9\right ) \, dx\\ &=\frac{343 (2+3 x)^5}{3645}-\frac{1862 (2+3 x)^6}{2187}+\frac{1657}{729} (2+3 x)^7-\frac{4099 (2+3 x)^8}{2916}+\frac{2180 (2+3 x)^9}{6561}-\frac{20}{729} (2+3 x)^{10}\\ \end{align*}

Mathematica [A]  time = 0.0023128, size = 57, normalized size = 0.85 \[ -1620 x^{10}-4260 x^9-\frac{9531 x^8}{4}+2823 x^7+\frac{10136 x^6}{3}-\frac{399 x^5}{5}-1386 x^4-\frac{1112 x^3}{3}+240 x^2+144 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^3*(2 + 3*x)^4*(3 + 5*x)^2,x]

[Out]

144*x + 240*x^2 - (1112*x^3)/3 - 1386*x^4 - (399*x^5)/5 + (10136*x^6)/3 + 2823*x^7 - (9531*x^8)/4 - 4260*x^9 -
1620*x^10

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Maple [A]  time = 0.001, size = 50, normalized size = 0.8 \begin{align*} -1620\,{x}^{10}-4260\,{x}^{9}-{\frac{9531\,{x}^{8}}{4}}+2823\,{x}^{7}+{\frac{10136\,{x}^{6}}{3}}-{\frac{399\,{x}^{5}}{5}}-1386\,{x}^{4}-{\frac{1112\,{x}^{3}}{3}}+240\,{x}^{2}+144\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^3*(2+3*x)^4*(3+5*x)^2,x)

[Out]

-1620*x^10-4260*x^9-9531/4*x^8+2823*x^7+10136/3*x^6-399/5*x^5-1386*x^4-1112/3*x^3+240*x^2+144*x

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Maxima [A]  time = 1.11194, size = 66, normalized size = 0.99 \begin{align*} -1620 \, x^{10} - 4260 \, x^{9} - \frac{9531}{4} \, x^{8} + 2823 \, x^{7} + \frac{10136}{3} \, x^{6} - \frac{399}{5} \, x^{5} - 1386 \, x^{4} - \frac{1112}{3} \, x^{3} + 240 \, x^{2} + 144 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^2,x, algorithm="maxima")

[Out]

-1620*x^10 - 4260*x^9 - 9531/4*x^8 + 2823*x^7 + 10136/3*x^6 - 399/5*x^5 - 1386*x^4 - 1112/3*x^3 + 240*x^2 + 14
4*x

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Fricas [A]  time = 0.925225, size = 155, normalized size = 2.31 \begin{align*} -1620 x^{10} - 4260 x^{9} - \frac{9531}{4} x^{8} + 2823 x^{7} + \frac{10136}{3} x^{6} - \frac{399}{5} x^{5} - 1386 x^{4} - \frac{1112}{3} x^{3} + 240 x^{2} + 144 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^2,x, algorithm="fricas")

[Out]

-1620*x^10 - 4260*x^9 - 9531/4*x^8 + 2823*x^7 + 10136/3*x^6 - 399/5*x^5 - 1386*x^4 - 1112/3*x^3 + 240*x^2 + 14
4*x

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Sympy [A]  time = 0.068607, size = 54, normalized size = 0.81 \begin{align*} - 1620 x^{10} - 4260 x^{9} - \frac{9531 x^{8}}{4} + 2823 x^{7} + \frac{10136 x^{6}}{3} - \frac{399 x^{5}}{5} - 1386 x^{4} - \frac{1112 x^{3}}{3} + 240 x^{2} + 144 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**3*(2+3*x)**4*(3+5*x)**2,x)

[Out]

-1620*x**10 - 4260*x**9 - 9531*x**8/4 + 2823*x**7 + 10136*x**6/3 - 399*x**5/5 - 1386*x**4 - 1112*x**3/3 + 240*
x**2 + 144*x

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Giac [A]  time = 2.93464, size = 66, normalized size = 0.99 \begin{align*} -1620 \, x^{10} - 4260 \, x^{9} - \frac{9531}{4} \, x^{8} + 2823 \, x^{7} + \frac{10136}{3} \, x^{6} - \frac{399}{5} \, x^{5} - 1386 \, x^{4} - \frac{1112}{3} \, x^{3} + 240 \, x^{2} + 144 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^3*(2+3*x)^4*(3+5*x)^2,x, algorithm="giac")

[Out]

-1620*x^10 - 4260*x^9 - 9531/4*x^8 + 2823*x^7 + 10136/3*x^6 - 399/5*x^5 - 1386*x^4 - 1112/3*x^3 + 240*x^2 + 14
4*x