3.1253 \(\int (1-2 x)^2 (2+3 x)^8 (3+5 x)^2 \, dx\)

Optimal. Leaf size=56 \[ \frac{100 (3 x+2)^{13}}{3159}-\frac{185}{729} (3 x+2)^{12}+\frac{503}{891} (3 x+2)^{11}-\frac{259 (3 x+2)^{10}}{1215}+\frac{49 (3 x+2)^9}{2187} \]

[Out]

(49*(2 + 3*x)^9)/2187 - (259*(2 + 3*x)^10)/1215 + (503*(2 + 3*x)^11)/891 - (185*(2 + 3*x)^12)/729 + (100*(2 +
3*x)^13)/3159

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Rubi [A]  time = 0.0313688, 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} \[ \frac{100 (3 x+2)^{13}}{3159}-\frac{185}{729} (3 x+2)^{12}+\frac{503}{891} (3 x+2)^{11}-\frac{259 (3 x+2)^{10}}{1215}+\frac{49 (3 x+2)^9}{2187} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^2,x]

[Out]

(49*(2 + 3*x)^9)/2187 - (259*(2 + 3*x)^10)/1215 + (503*(2 + 3*x)^11)/891 - (185*(2 + 3*x)^12)/729 + (100*(2 +
3*x)^13)/3159

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)^8 (3+5 x)^2 \, dx &=\int \left (\frac{49}{81} (2+3 x)^8-\frac{518}{81} (2+3 x)^9+\frac{503}{27} (2+3 x)^{10}-\frac{740}{81} (2+3 x)^{11}+\frac{100}{81} (2+3 x)^{12}\right ) \, dx\\ &=\frac{49 (2+3 x)^9}{2187}-\frac{259 (2+3 x)^{10}}{1215}+\frac{503}{891} (2+3 x)^{11}-\frac{185}{729} (2+3 x)^{12}+\frac{100 (2+3 x)^{13}}{3159}\\ \end{align*}

Mathematica [A]  time = 0.0029319, size = 74, normalized size = 1.32 \[ \frac{656100 x^{13}}{13}+302535 x^{12}+\frac{8477541 x^{11}}{11}+\frac{5207733 x^{10}}{5}+697905 x^9+6858 x^8-384336 x^7-298240 x^6-\frac{338336 x^5}{5}+40640 x^4+\frac{111616 x^3}{3}+13056 x^2+2304 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^8*(3 + 5*x)^2,x]

[Out]

2304*x + 13056*x^2 + (111616*x^3)/3 + 40640*x^4 - (338336*x^5)/5 - 298240*x^6 - 384336*x^7 + 6858*x^8 + 697905
*x^9 + (5207733*x^10)/5 + (8477541*x^11)/11 + 302535*x^12 + (656100*x^13)/13

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Maple [A]  time = 0.002, size = 65, normalized size = 1.2 \begin{align*}{\frac{656100\,{x}^{13}}{13}}+302535\,{x}^{12}+{\frac{8477541\,{x}^{11}}{11}}+{\frac{5207733\,{x}^{10}}{5}}+697905\,{x}^{9}+6858\,{x}^{8}-384336\,{x}^{7}-298240\,{x}^{6}-{\frac{338336\,{x}^{5}}{5}}+40640\,{x}^{4}+{\frac{111616\,{x}^{3}}{3}}+13056\,{x}^{2}+2304\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^8*(3+5*x)^2,x)

[Out]

656100/13*x^13+302535*x^12+8477541/11*x^11+5207733/5*x^10+697905*x^9+6858*x^8-384336*x^7-298240*x^6-338336/5*x
^5+40640*x^4+111616/3*x^3+13056*x^2+2304*x

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Maxima [A]  time = 1.06466, size = 86, normalized size = 1.54 \begin{align*} \frac{656100}{13} \, x^{13} + 302535 \, x^{12} + \frac{8477541}{11} \, x^{11} + \frac{5207733}{5} \, x^{10} + 697905 \, x^{9} + 6858 \, x^{8} - 384336 \, x^{7} - 298240 \, x^{6} - \frac{338336}{5} \, x^{5} + 40640 \, x^{4} + \frac{111616}{3} \, x^{3} + 13056 \, x^{2} + 2304 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x)^2,x, algorithm="maxima")

[Out]

656100/13*x^13 + 302535*x^12 + 8477541/11*x^11 + 5207733/5*x^10 + 697905*x^9 + 6858*x^8 - 384336*x^7 - 298240*
x^6 - 338336/5*x^5 + 40640*x^4 + 111616/3*x^3 + 13056*x^2 + 2304*x

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Fricas [A]  time = 1.32728, size = 240, normalized size = 4.29 \begin{align*} \frac{656100}{13} x^{13} + 302535 x^{12} + \frac{8477541}{11} x^{11} + \frac{5207733}{5} x^{10} + 697905 x^{9} + 6858 x^{8} - 384336 x^{7} - 298240 x^{6} - \frac{338336}{5} x^{5} + 40640 x^{4} + \frac{111616}{3} x^{3} + 13056 x^{2} + 2304 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x)^2,x, algorithm="fricas")

[Out]

656100/13*x^13 + 302535*x^12 + 8477541/11*x^11 + 5207733/5*x^10 + 697905*x^9 + 6858*x^8 - 384336*x^7 - 298240*
x^6 - 338336/5*x^5 + 40640*x^4 + 111616/3*x^3 + 13056*x^2 + 2304*x

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Sympy [A]  time = 0.073572, size = 71, normalized size = 1.27 \begin{align*} \frac{656100 x^{13}}{13} + 302535 x^{12} + \frac{8477541 x^{11}}{11} + \frac{5207733 x^{10}}{5} + 697905 x^{9} + 6858 x^{8} - 384336 x^{7} - 298240 x^{6} - \frac{338336 x^{5}}{5} + 40640 x^{4} + \frac{111616 x^{3}}{3} + 13056 x^{2} + 2304 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**8*(3+5*x)**2,x)

[Out]

656100*x**13/13 + 302535*x**12 + 8477541*x**11/11 + 5207733*x**10/5 + 697905*x**9 + 6858*x**8 - 384336*x**7 -
298240*x**6 - 338336*x**5/5 + 40640*x**4 + 111616*x**3/3 + 13056*x**2 + 2304*x

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Giac [A]  time = 3.87469, size = 86, normalized size = 1.54 \begin{align*} \frac{656100}{13} \, x^{13} + 302535 \, x^{12} + \frac{8477541}{11} \, x^{11} + \frac{5207733}{5} \, x^{10} + 697905 \, x^{9} + 6858 \, x^{8} - 384336 \, x^{7} - 298240 \, x^{6} - \frac{338336}{5} \, x^{5} + 40640 \, x^{4} + \frac{111616}{3} \, x^{3} + 13056 \, x^{2} + 2304 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^8*(3+5*x)^2,x, algorithm="giac")

[Out]

656100/13*x^13 + 302535*x^12 + 8477541/11*x^11 + 5207733/5*x^10 + 697905*x^9 + 6858*x^8 - 384336*x^7 - 298240*
x^6 - 338336/5*x^5 + 40640*x^4 + 111616/3*x^3 + 13056*x^2 + 2304*x