3.1255 \(\int (1-2 x)^2 (2+3 x)^6 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ \frac{100 (3 x+2)^{11}}{2673}-\frac{74}{243} (3 x+2)^{10}+\frac{503}{729} (3 x+2)^9-\frac{259}{972} (3 x+2)^8+\frac{7}{243} (3 x+2)^7 \]

[Out]

(7*(2 + 3*x)^7)/243 - (259*(2 + 3*x)^8)/972 + (503*(2 + 3*x)^9)/729 - (74*(2 + 3*x)^10)/243 + (100*(2 + 3*x)^1
1)/2673

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Rubi [A]  time = 0.0269701, 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} \[ \frac{100 (3 x+2)^{11}}{2673}-\frac{74}{243} (3 x+2)^{10}+\frac{503}{729} (3 x+2)^9-\frac{259}{972} (3 x+2)^8+\frac{7}{243} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^2,x]

[Out]

(7*(2 + 3*x)^7)/243 - (259*(2 + 3*x)^8)/972 + (503*(2 + 3*x)^9)/729 - (74*(2 + 3*x)^10)/243 + (100*(2 + 3*x)^1
1)/2673

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)^6 (3+5 x)^2 \, dx &=\int \left (\frac{49}{81} (2+3 x)^6-\frac{518}{81} (2+3 x)^7+\frac{503}{27} (2+3 x)^8-\frac{740}{81} (2+3 x)^9+\frac{100}{81} (2+3 x)^{10}\right ) \, dx\\ &=\frac{7}{243} (2+3 x)^7-\frac{259}{972} (2+3 x)^8+\frac{503}{729} (2+3 x)^9-\frac{74}{243} (2+3 x)^{10}+\frac{100 (2+3 x)^{11}}{2673}\\ \end{align*}

Mathematica [A]  time = 0.0021563, size = 60, normalized size = 1.07 \[ \frac{72900 x^{11}}{11}+30618 x^{10}+55701 x^9+\frac{176391 x^8}{4}+675 x^7-26166 x^6-18340 x^5-1696 x^4+\frac{12208 x^3}{3}+2400 x^2+576 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^6*(3 + 5*x)^2,x]

[Out]

576*x + 2400*x^2 + (12208*x^3)/3 - 1696*x^4 - 18340*x^5 - 26166*x^6 + 675*x^7 + (176391*x^8)/4 + 55701*x^9 + 3
0618*x^10 + (72900*x^11)/11

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Maple [A]  time = 0.002, size = 55, normalized size = 1. \begin{align*}{\frac{72900\,{x}^{11}}{11}}+30618\,{x}^{10}+55701\,{x}^{9}+{\frac{176391\,{x}^{8}}{4}}+675\,{x}^{7}-26166\,{x}^{6}-18340\,{x}^{5}-1696\,{x}^{4}+{\frac{12208\,{x}^{3}}{3}}+2400\,{x}^{2}+576\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x)

[Out]

72900/11*x^11+30618*x^10+55701*x^9+176391/4*x^8+675*x^7-26166*x^6-18340*x^5-1696*x^4+12208/3*x^3+2400*x^2+576*
x

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Maxima [A]  time = 1.10157, size = 73, normalized size = 1.3 \begin{align*} \frac{72900}{11} \, x^{11} + 30618 \, x^{10} + 55701 \, x^{9} + \frac{176391}{4} \, x^{8} + 675 \, x^{7} - 26166 \, x^{6} - 18340 \, x^{5} - 1696 \, x^{4} + \frac{12208}{3} \, x^{3} + 2400 \, x^{2} + 576 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x, algorithm="maxima")

[Out]

72900/11*x^11 + 30618*x^10 + 55701*x^9 + 176391/4*x^8 + 675*x^7 - 26166*x^6 - 18340*x^5 - 1696*x^4 + 12208/3*x
^3 + 2400*x^2 + 576*x

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Fricas [A]  time = 1.31469, size = 180, normalized size = 3.21 \begin{align*} \frac{72900}{11} x^{11} + 30618 x^{10} + 55701 x^{9} + \frac{176391}{4} x^{8} + 675 x^{7} - 26166 x^{6} - 18340 x^{5} - 1696 x^{4} + \frac{12208}{3} x^{3} + 2400 x^{2} + 576 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x, algorithm="fricas")

[Out]

72900/11*x^11 + 30618*x^10 + 55701*x^9 + 176391/4*x^8 + 675*x^7 - 26166*x^6 - 18340*x^5 - 1696*x^4 + 12208/3*x
^3 + 2400*x^2 + 576*x

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Sympy [A]  time = 0.070096, size = 58, normalized size = 1.04 \begin{align*} \frac{72900 x^{11}}{11} + 30618 x^{10} + 55701 x^{9} + \frac{176391 x^{8}}{4} + 675 x^{7} - 26166 x^{6} - 18340 x^{5} - 1696 x^{4} + \frac{12208 x^{3}}{3} + 2400 x^{2} + 576 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**6*(3+5*x)**2,x)

[Out]

72900*x**11/11 + 30618*x**10 + 55701*x**9 + 176391*x**8/4 + 675*x**7 - 26166*x**6 - 18340*x**5 - 1696*x**4 + 1
2208*x**3/3 + 2400*x**2 + 576*x

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Giac [A]  time = 1.73218, size = 73, normalized size = 1.3 \begin{align*} \frac{72900}{11} \, x^{11} + 30618 \, x^{10} + 55701 \, x^{9} + \frac{176391}{4} \, x^{8} + 675 \, x^{7} - 26166 \, x^{6} - 18340 \, x^{5} - 1696 \, x^{4} + \frac{12208}{3} \, x^{3} + 2400 \, x^{2} + 576 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^6*(3+5*x)^2,x, algorithm="giac")

[Out]

72900/11*x^11 + 30618*x^10 + 55701*x^9 + 176391/4*x^8 + 675*x^7 - 26166*x^6 - 18340*x^5 - 1696*x^4 + 12208/3*x
^3 + 2400*x^2 + 576*x