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

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

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Rubi [A]  time = 0.04, antiderivative size = 67, normalized size of antiderivative = 1.00, 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} \begin {gather*} \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} \end {gather*}

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*}

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Mathematica [A]  time = 0.00, size = 93, normalized size = 1.39 \begin {gather*} \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 {gather*}

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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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^2 (2+3 x)^{10} (3+5 x)^3 \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.56, size = 79, normalized size = 1.18 \begin {gather*} \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 {gather*}

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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giac [A]  time = 0.95, size = 79, normalized size = 1.18 \begin {gather*} \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 {gather*}

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

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maple [A]  time = 0.00, size = 80, normalized size = 1.19 \begin {gather*} \frac {7381125}{4} x^{16}[phone] x^{15}+\frac {734077485}{14} x^{14}+\frac {1417418757}{13} x^{13}+\frac {569034801}{4} x^{12}+\frac {1233925083}{11} x^{11}[phone] 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 {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^2*(3*x+2)^10*(5*x+3)^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 = 0.51, size = 79, normalized size = 1.18 \begin {gather*} \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 {gather*}

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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mupad [B]  time = 0.15, size = 79, normalized size = 1.18 \begin {gather*} \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 {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x - 1)^2*(3*x + 2)^10*(5*x + 3)^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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sympy [A]  time = 0.09, size = 90, normalized size = 1.34 \begin {gather*} \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 {gather*}

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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