3.1256 \(\int (1-2 x)^2 (2+3 x)^5 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ \frac{10}{243} (3 x+2)^{10}-\frac{740 (3 x+2)^9}{2187}+\frac{503}{648} (3 x+2)^8-\frac{74}{243} (3 x+2)^7+\frac{49 (3 x+2)^6}{1458} \]

[Out]

(49*(2 + 3*x)^6)/1458 - (74*(2 + 3*x)^7)/243 + (503*(2 + 3*x)^8)/648 - (740*(2 + 3*x)^9)/2187 + (10*(2 + 3*x)^
10)/243

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Rubi [A]  time = 0.0249215, antiderivative size = 56, 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} \[ \frac{10}{243} (3 x+2)^{10}-\frac{740 (3 x+2)^9}{2187}+\frac{503}{648} (3 x+2)^8-\frac{74}{243} (3 x+2)^7+\frac{49 (3 x+2)^6}{1458} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(49*(2 + 3*x)^6)/1458 - (74*(2 + 3*x)^7)/243 + (503*(2 + 3*x)^8)/648 - (740*(2 + 3*x)^9)/2187 + (10*(2 + 3*x)^
10)/243

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)^5 (3+5 x)^2 \, dx &=\int \left (\frac{49}{81} (2+3 x)^5-\frac{518}{81} (2+3 x)^6+\frac{503}{27} (2+3 x)^7-\frac{740}{81} (2+3 x)^8+\frac{100}{81} (2+3 x)^9\right ) \, dx\\ &=\frac{49 (2+3 x)^6}{1458}-\frac{74}{243} (2+3 x)^7+\frac{503}{648} (2+3 x)^8-\frac{740 (2+3 x)^9}{2187}+\frac{10}{243} (2+3 x)^{10}\\ \end{align*}

Mathematica [A]  time = 0.0019774, size = 55, normalized size = 0.98 \[ 2430 x^{10}+9540 x^9+\frac{109863 x^8}{8}+6336 x^7-\frac{9331 x^6}{2}-6734 x^5-2030 x^4+\frac{3152 x^3}{3}+984 x^2+288 x \]

Antiderivative was successfully verified.

[In]

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

[Out]

288*x + 984*x^2 + (3152*x^3)/3 - 2030*x^4 - 6734*x^5 - (9331*x^6)/2 + 6336*x^7 + (109863*x^8)/8 + 9540*x^9 + 2
430*x^10

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Maple [A]  time = 0.002, size = 50, normalized size = 0.9 \begin{align*} 2430\,{x}^{10}+9540\,{x}^{9}+{\frac{109863\,{x}^{8}}{8}}+6336\,{x}^{7}-{\frac{9331\,{x}^{6}}{2}}-6734\,{x}^{5}-2030\,{x}^{4}+{\frac{3152\,{x}^{3}}{3}}+984\,{x}^{2}+288\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2430*x^10+9540*x^9+109863/8*x^8+6336*x^7-9331/2*x^6-6734*x^5-2030*x^4+3152/3*x^3+984*x^2+288*x

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Maxima [A]  time = 2.36112, size = 66, normalized size = 1.18 \begin{align*} 2430 \, x^{10} + 9540 \, x^{9} + \frac{109863}{8} \, x^{8} + 6336 \, x^{7} - \frac{9331}{2} \, x^{6} - 6734 \, x^{5} - 2030 \, x^{4} + \frac{3152}{3} \, x^{3} + 984 \, x^{2} + 288 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2430*x^10 + 9540*x^9 + 109863/8*x^8 + 6336*x^7 - 9331/2*x^6 - 6734*x^5 - 2030*x^4 + 3152/3*x^3 + 984*x^2 + 288
*x

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Fricas [A]  time = 1.23825, size = 154, normalized size = 2.75 \begin{align*} 2430 x^{10} + 9540 x^{9} + \frac{109863}{8} x^{8} + 6336 x^{7} - \frac{9331}{2} x^{6} - 6734 x^{5} - 2030 x^{4} + \frac{3152}{3} x^{3} + 984 x^{2} + 288 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2430*x^10 + 9540*x^9 + 109863/8*x^8 + 6336*x^7 - 9331/2*x^6 - 6734*x^5 - 2030*x^4 + 3152/3*x^3 + 984*x^2 + 288
*x

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Sympy [A]  time = 0.068971, size = 53, normalized size = 0.95 \begin{align*} 2430 x^{10} + 9540 x^{9} + \frac{109863 x^{8}}{8} + 6336 x^{7} - \frac{9331 x^{6}}{2} - 6734 x^{5} - 2030 x^{4} + \frac{3152 x^{3}}{3} + 984 x^{2} + 288 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2430*x**10 + 9540*x**9 + 109863*x**8/8 + 6336*x**7 - 9331*x**6/2 - 6734*x**5 - 2030*x**4 + 3152*x**3/3 + 984*x
**2 + 288*x

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Giac [A]  time = 1.81899, size = 66, normalized size = 1.18 \begin{align*} 2430 \, x^{10} + 9540 \, x^{9} + \frac{109863}{8} \, x^{8} + 6336 \, x^{7} - \frac{9331}{2} \, x^{6} - 6734 \, x^{5} - 2030 \, x^{4} + \frac{3152}{3} \, x^{3} + 984 \, x^{2} + 288 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2430*x^10 + 9540*x^9 + 109863/8*x^8 + 6336*x^7 - 9331/2*x^6 - 6734*x^5 - 2030*x^4 + 3152/3*x^3 + 984*x^2 + 288
*x