3.1158 \(\int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx\)

Optimal. Leaf size=56 \[ -\frac{250 (3 x+2)^{13}}{3159}+\frac{1025 (3 x+2)^{12}}{2916}-\frac{185}{891} (3 x+2)^{11}+\frac{107 (3 x+2)^{10}}{2430}-\frac{7 (3 x+2)^9}{2187} \]

[Out]

(-7*(2 + 3*x)^9)/2187 + (107*(2 + 3*x)^10)/2430 - (185*(2 + 3*x)^11)/891 + (1025
*(2 + 3*x)^12)/2916 - (250*(2 + 3*x)^13)/3159

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Rubi [A]  time = 0.0927637, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{250 (3 x+2)^{13}}{3159}+\frac{1025 (3 x+2)^{12}}{2916}-\frac{185}{891} (3 x+2)^{11}+\frac{107 (3 x+2)^{10}}{2430}-\frac{7 (3 x+2)^9}{2187} \]

Antiderivative was successfully verified.

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

[Out]

(-7*(2 + 3*x)^9)/2187 + (107*(2 + 3*x)^10)/2430 - (185*(2 + 3*x)^11)/891 + (1025
*(2 + 3*x)^12)/2916 - (250*(2 + 3*x)^13)/3159

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Rubi in Sympy [A]  time = 14.0084, size = 49, normalized size = 0.88 \[ - \frac{250 \left (3 x + 2\right )^{13}}{3159} + \frac{1025 \left (3 x + 2\right )^{12}}{2916} - \frac{185 \left (3 x + 2\right )^{11}}{891} + \frac{107 \left (3 x + 2\right )^{10}}{2430} - \frac{7 \left (3 x + 2\right )^{9}}{2187} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(2+3*x)**8*(3+5*x)**3,x)

[Out]

-250*(3*x + 2)**13/3159 + 1025*(3*x + 2)**12/2916 - 185*(3*x + 2)**11/891 + 107*
(3*x + 2)**10/2430 - 7*(3*x + 2)**9/2187

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Mathematica [A]  time = 0.00358125, size = 74, normalized size = 1.32 \[ -\frac{1640250 x^{13}}{13}-\frac{3626775 x^{12}}{4}-\frac{32079645 x^{11}}{11}-\frac{54794799 x^{10}}{10}-6524829 x^9-4865076 x^8-1830960 x^7+350128 x^6+\frac{4580384 x^5}{5}+597824 x^4+224256 x^3+51840 x^2+6912 x \]

Antiderivative was successfully verified.

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

[Out]

6912*x + 51840*x^2 + 224256*x^3 + 597824*x^4 + (4580384*x^5)/5 + 350128*x^6 - 18
30960*x^7 - 4865076*x^8 - 6524829*x^9 - (54794799*x^10)/10 - (32079645*x^11)/11
- (3626775*x^12)/4 - (1640250*x^13)/13

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Maple [A]  time = 0.003, size = 65, normalized size = 1.2 \[ -{\frac{1640250\,{x}^{13}}{13}}-{\frac{3626775\,{x}^{12}}{4}}-{\frac{32079645\,{x}^{11}}{11}}-{\frac{54794799\,{x}^{10}}{10}}-6524829\,{x}^{9}-4865076\,{x}^{8}-1830960\,{x}^{7}+350128\,{x}^{6}+{\frac{4580384\,{x}^{5}}{5}}+597824\,{x}^{4}+224256\,{x}^{3}+51840\,{x}^{2}+6912\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1640250/13*x^13-3626775/4*x^12-32079645/11*x^11-54794799/10*x^10-6524829*x^9-48
65076*x^8-1830960*x^7+350128*x^6+4580384/5*x^5+597824*x^4+224256*x^3+51840*x^2+6
912*x

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Maxima [A]  time = 1.34306, size = 86, normalized size = 1.54 \[ -\frac{1640250}{13} \, x^{13} - \frac{3626775}{4} \, x^{12} - \frac{32079645}{11} \, x^{11} - \frac{54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac{4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1640250/13*x^13 - 3626775/4*x^12 - 32079645/11*x^11 - 54794799/10*x^10 - 652482
9*x^9 - 4865076*x^8 - 1830960*x^7 + 350128*x^6 + 4580384/5*x^5 + 597824*x^4 + 22
4256*x^3 + 51840*x^2 + 6912*x

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Fricas [A]  time = 0.186057, size = 1, normalized size = 0.02 \[ -\frac{1640250}{13} x^{13} - \frac{3626775}{4} x^{12} - \frac{32079645}{11} x^{11} - \frac{54794799}{10} x^{10} - 6524829 x^{9} - 4865076 x^{8} - 1830960 x^{7} + 350128 x^{6} + \frac{4580384}{5} x^{5} + 597824 x^{4} + 224256 x^{3} + 51840 x^{2} + 6912 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1640250/13*x^13 - 3626775/4*x^12 - 32079645/11*x^11 - 54794799/10*x^10 - 652482
9*x^9 - 4865076*x^8 - 1830960*x^7 + 350128*x^6 + 4580384/5*x^5 + 597824*x^4 + 22
4256*x^3 + 51840*x^2 + 6912*x

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Sympy [A]  time = 0.120772, size = 71, normalized size = 1.27 \[ - \frac{1640250 x^{13}}{13} - \frac{3626775 x^{12}}{4} - \frac{32079645 x^{11}}{11} - \frac{54794799 x^{10}}{10} - 6524829 x^{9} - 4865076 x^{8} - 1830960 x^{7} + 350128 x^{6} + \frac{4580384 x^{5}}{5} + 597824 x^{4} + 224256 x^{3} + 51840 x^{2} + 6912 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1640250*x**13/13 - 3626775*x**12/4 - 32079645*x**11/11 - 54794799*x**10/10 - 65
24829*x**9 - 4865076*x**8 - 1830960*x**7 + 350128*x**6 + 4580384*x**5/5 + 597824
*x**4 + 224256*x**3 + 51840*x**2 + 6912*x

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GIAC/XCAS [A]  time = 0.206994, size = 86, normalized size = 1.54 \[ -\frac{1640250}{13} \, x^{13} - \frac{3626775}{4} \, x^{12} - \frac{32079645}{11} \, x^{11} - \frac{54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac{4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1640250/13*x^13 - 3626775/4*x^12 - 32079645/11*x^11 - 54794799/10*x^10 - 652482
9*x^9 - 4865076*x^8 - 1830960*x^7 + 350128*x^6 + 4580384/5*x^5 + 597824*x^4 + 22
4256*x^3 + 51840*x^2 + 6912*x