3.1270 \(\int (1-2 x)^2 (2+3 x)^{10} (3+5 x)^3 \, dx\)

Optimal. Leaf size=67 \[ \frac{125 (3 x+2)^{16}}{2916}-\frac{760 (3 x+2)^{15}}{2187}+\frac{8285 (3 x+2)^{14}}{10206}-\frac{4099 (3 x+2)^{13}}{9477}+\frac{763 (3 x+2)^{12}}{8748}-\frac{49 (3 x+2)^{11}}{8019} \]

[Out]

(-49*(2 + 3*x)^11)/8019 + (763*(2 + 3*x)^12)/8748 - (4099*(2 + 3*x)^13)/9477 + (8285*(2 + 3*x)^14)/10206 - (76
0*(2 + 3*x)^15)/2187 + (125*(2 + 3*x)^16)/2916

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Rubi [A]  time = 0.0388608, 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} \[ \frac{125 (3 x+2)^{16}}{2916}-\frac{760 (3 x+2)^{15}}{2187}+\frac{8285 (3 x+2)^{14}}{10206}-\frac{4099 (3 x+2)^{13}}{9477}+\frac{763 (3 x+2)^{12}}{8748}-\frac{49 (3 x+2)^{11}}{8019} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^2*(2 + 3*x)^10*(3 + 5*x)^3,x]

[Out]

(-49*(2 + 3*x)^11)/8019 + (763*(2 + 3*x)^12)/8748 - (4099*(2 + 3*x)^13)/9477 + (8285*(2 + 3*x)^14)/10206 - (76
0*(2 + 3*x)^15)/2187 + (125*(2 + 3*x)^16)/2916

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)^{10} (3+5 x)^3 \, dx &=\int \left (-\frac{49}{243} (2+3 x)^{10}+\frac{763}{243} (2+3 x)^{11}-\frac{4099}{243} (2+3 x)^{12}+\frac{8285}{243} (2+3 x)^{13}-\frac{3800}{243} (2+3 x)^{14}+\frac{500}{243} (2+3 x)^{15}\right ) \, dx\\ &=-\frac{49 (2+3 x)^{11}}{8019}+\frac{763 (2+3 x)^{12}}{8748}-\frac{4099 (2+3 x)^{13}}{9477}+\frac{8285 (2+3 x)^{14}}{10206}-\frac{760 (2+3 x)^{15}}{2187}+\frac{125 (2+3 x)^{16}}{2916}\\ \end{align*}

Mathematica [A]  time = 0.00337, size = 93, normalized size = 1.39 \[ \frac{7381125 x^{16}}{4}[phone] x^{15}+\frac{734077485 x^{14}}{14}+\frac{1417418757 x^{13}}{13}+\frac{569034801 x^{12}}{4}+\frac{1233925083 x^{11}}{11}[phone] x^{10}-26237700 x^9-40113468 x^8-\frac{154612896 x^7}{7}-\frac{10627328 x^6}{3}+3185792 x^5+2644160 x^4+1000704 x^3+221184 x^2+27648 x \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^2*(2 + 3*x)^10*(3 + 5*x)^3,x]

[Out]

27648*x + 221184*x^2 + 1000704*x^3 + 2644160*x^4 + 3185792*x^5 - (10627328*x^6)/3 - (154612896*x^7)/7 - 401134
68*x^8 - 26237700*x^9 + 36043704*x^10 + (1233925083*x^11)/11 + (569034801*x^12)/4 + (1417418757*x^13)/13 + (73
4077485*x^14)/14 + 14696640*x^15 + (7381125*x^16)/4

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Maple [A]  time = 0.001, size = 80, normalized size = 1.2 \begin{align*}{\frac{7381125\,{x}^{16}}{4}}[phone]\,{x}^{15}+{\frac{734077485\,{x}^{14}}{14}}+{\frac{1417418757\,{x}^{13}}{13}}+{\frac{569034801\,{x}^{12}}{4}}+{\frac{1233925083\,{x}^{11}}{11}}[phone]\,{x}^{10}-26237700\,{x}^{9}-40113468\,{x}^{8}-{\frac{154612896\,{x}^{7}}{7}}-{\frac{10627328\,{x}^{6}}{3}}+3185792\,{x}^{5}+2644160\,{x}^{4}+1000704\,{x}^{3}+221184\,{x}^{2}+27648\,x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(2+3*x)^10*(3+5*x)^3,x)

[Out]

7381125/4*x^16+14696640*x^15+734077485/14*x^14+1417418757/13*x^13+569034801/4*x^12+1233925083/11*x^11+36043704
*x^10-26237700*x^9-40113468*x^8-154612896/7*x^7-10627328/3*x^6+3185792*x^5+2644160*x^4+1000704*x^3+221184*x^2+
27648*x

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Maxima [A]  time = 1.02317, size = 107, normalized size = 1.6 \begin{align*} \frac{7381125}{4} \, x^{16} + 14696640 \, x^{15} + \frac{734077485}{14} \, x^{14} + \frac{1417418757}{13} \, x^{13} + \frac{569034801}{4} \, x^{12} + \frac{1233925083}{11} \, x^{11} + 36043704 \, x^{10} - 26237700 \, x^{9} - 40113468 \, x^{8} - \frac{154612896}{7} \, x^{7} - \frac{10627328}{3} \, x^{6} + 3185792 \, x^{5} + 2644160 \, x^{4} + 1000704 \, x^{3} + 221184 \, x^{2} + 27648 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^10*(3+5*x)^3,x, algorithm="maxima")

[Out]

7381125/4*x^16 + 14696640*x^15 + 734077485/14*x^14 + 1417418757/13*x^13 + 569034801/4*x^12 + 1233925083/11*x^1
1 + 36043704*x^10 - 26237700*x^9 - 40113468*x^8 - 154612896/7*x^7 - 10627328/3*x^6 + 3185792*x^5 + 2644160*x^4
+ 1000704*x^3 + 221184*x^2 + 27648*x

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Fricas [A]  time = 1.4583, size = 350, normalized size = 5.22 \begin{align*} \frac{7381125}{4} x^{16} + 14696640 x^{15} + \frac{734077485}{14} x^{14} + \frac{1417418757}{13} x^{13} + \frac{569034801}{4} x^{12} + \frac{1233925083}{11} x^{11} + 36043704 x^{10} - 26237700 x^{9} - 40113468 x^{8} - \frac{154612896}{7} x^{7} - \frac{10627328}{3} x^{6} + 3185792 x^{5} + 2644160 x^{4} + 1000704 x^{3} + 221184 x^{2} + 27648 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^10*(3+5*x)^3,x, algorithm="fricas")

[Out]

7381125/4*x^16 + 14696640*x^15 + 734077485/14*x^14 + 1417418757/13*x^13 + 569034801/4*x^12 + 1233925083/11*x^1
1 + 36043704*x^10 - 26237700*x^9 - 40113468*x^8 - 154612896/7*x^7 - 10627328/3*x^6 + 3185792*x^5 + 2644160*x^4
+ 1000704*x^3 + 221184*x^2 + 27648*x

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Sympy [A]  time = 0.08273, size = 90, normalized size = 1.34 \begin{align*} \frac{7381125 x^{16}}{4} + 14696640 x^{15} + \frac{734077485 x^{14}}{14} + \frac{1417418757 x^{13}}{13} + \frac{569034801 x^{12}}{4} + \frac{1233925083 x^{11}}{11} + 36043704 x^{10} - 26237700 x^{9} - 40113468 x^{8} - \frac{154612896 x^{7}}{7} - \frac{10627328 x^{6}}{3} + 3185792 x^{5} + 2644160 x^{4} + 1000704 x^{3} + 221184 x^{2} + 27648 x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**2*(2+3*x)**10*(3+5*x)**3,x)

[Out]

7381125*x**16/4 + 14696640*x**15 + 734077485*x**14/14 + 1417418757*x**13/13 + 569034801*x**12/4 + 1233925083*x
**11/11 + 36043704*x**10 - 26237700*x**9 - 40113468*x**8 - 154612896*x**7/7 - 10627328*x**6/3 + 3185792*x**5 +
2644160*x**4 + 1000704*x**3 + 221184*x**2 + 27648*x

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Giac [A]  time = 1.6064, size = 107, normalized size = 1.6 \begin{align*} \frac{7381125}{4} \, x^{16} + 14696640 \, x^{15} + \frac{734077485}{14} \, x^{14} + \frac{1417418757}{13} \, x^{13} + \frac{569034801}{4} \, x^{12} + \frac{1233925083}{11} \, x^{11} + 36043704 \, x^{10} - 26237700 \, x^{9} - 40113468 \, x^{8} - \frac{154612896}{7} \, x^{7} - \frac{10627328}{3} \, x^{6} + 3185792 \, x^{5} + 2644160 \, x^{4} + 1000704 \, x^{3} + 221184 \, x^{2} + 27648 \, x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^2*(2+3*x)^10*(3+5*x)^3,x, algorithm="giac")

[Out]

7381125/4*x^16 + 14696640*x^15 + 734077485/14*x^14 + 1417418757/13*x^13 + 569034801/4*x^12 + 1233925083/11*x^1
1 + 36043704*x^10 - 26237700*x^9 - 40113468*x^8 - 154612896/7*x^7 - 10627328/3*x^6 + 3185792*x^5 + 2644160*x^4
+ 1000704*x^3 + 221184*x^2 + 27648*x