3.1159 \(\int (1-2 x) (2+3 x)^7 (3+5 x)^3 \, dx\)

Optimal. Leaf size=56 \[ -\frac{125 (3 x+2)^{12}}{1458}+\frac{1025 (3 x+2)^{11}}{2673}-\frac{37}{162} (3 x+2)^{10}+\frac{107 (3 x+2)^9}{2187}-\frac{7 (3 x+2)^8}{1944} \]

[Out]

(-7*(2 + 3*x)^8)/1944 + (107*(2 + 3*x)^9)/2187 - (37*(2 + 3*x)^10)/162 + (1025*(
2 + 3*x)^11)/2673 - (125*(2 + 3*x)^12)/1458

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Rubi [A]  time = 0.0901101, 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 \[ -\frac{125 (3 x+2)^{12}}{1458}+\frac{1025 (3 x+2)^{11}}{2673}-\frac{37}{162} (3 x+2)^{10}+\frac{107 (3 x+2)^9}{2187}-\frac{7 (3 x+2)^8}{1944} \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)^3,x]

[Out]

(-7*(2 + 3*x)^8)/1944 + (107*(2 + 3*x)^9)/2187 - (37*(2 + 3*x)^10)/162 + (1025*(
2 + 3*x)^11)/2673 - (125*(2 + 3*x)^12)/1458

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Rubi in Sympy [A]  time = 13.2293, size = 49, normalized size = 0.88 \[ - \frac{125 \left (3 x + 2\right )^{12}}{1458} + \frac{1025 \left (3 x + 2\right )^{11}}{2673} - \frac{37 \left (3 x + 2\right )^{10}}{162} + \frac{107 \left (3 x + 2\right )^{9}}{2187} - \frac{7 \left (3 x + 2\right )^{8}}{1944} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)*(2+3*x)**7*(3+5*x)**3,x)

[Out]

-125*(3*x + 2)**12/1458 + 1025*(3*x + 2)**11/2673 - 37*(3*x + 2)**10/162 + 107*(
3*x + 2)**9/2187 - 7*(3*x + 2)**8/1944

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Mathematica [A]  time = 0.00333838, size = 67, normalized size = 1.2 \[ -\frac{91125 x^{12}}{2}-\frac{3262275 x^{11}}{11}-\frac{1703673 x^{10}}{2}-1398447 x^9-\frac{11183805 x^8}{8}-788238 x^7-98966 x^6+219224 x^5+199012 x^4+88800 x^3+23328 x^2+3456 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)*(2 + 3*x)^7*(3 + 5*x)^3,x]

[Out]

3456*x + 23328*x^2 + 88800*x^3 + 199012*x^4 + 219224*x^5 - 98966*x^6 - 788238*x^
7 - (11183805*x^8)/8 - 1398447*x^9 - (1703673*x^10)/2 - (3262275*x^11)/11 - (911
25*x^12)/2

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Maple [A]  time = 0.002, size = 60, normalized size = 1.1 \[ -{\frac{91125\,{x}^{12}}{2}}-{\frac{3262275\,{x}^{11}}{11}}-{\frac{1703673\,{x}^{10}}{2}}-1398447\,{x}^{9}-{\frac{11183805\,{x}^{8}}{8}}-788238\,{x}^{7}-98966\,{x}^{6}+219224\,{x}^{5}+199012\,{x}^{4}+88800\,{x}^{3}+23328\,{x}^{2}+3456\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)*(2+3*x)^7*(3+5*x)^3,x)

[Out]

-91125/2*x^12-3262275/11*x^11-1703673/2*x^10-1398447*x^9-11183805/8*x^8-788238*x
^7-98966*x^6+219224*x^5+199012*x^4+88800*x^3+23328*x^2+3456*x

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Maxima [A]  time = 1.35338, size = 80, normalized size = 1.43 \[ -\frac{91125}{2} \, x^{12} - \frac{3262275}{11} \, x^{11} - \frac{1703673}{2} \, x^{10} - 1398447 \, x^{9} - \frac{11183805}{8} \, x^{8} - 788238 \, x^{7} - 98966 \, x^{6} + 219224 \, x^{5} + 199012 \, x^{4} + 88800 \, x^{3} + 23328 \, x^{2} + 3456 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^7*(2*x - 1),x, algorithm="maxima")

[Out]

-91125/2*x^12 - 3262275/11*x^11 - 1703673/2*x^10 - 1398447*x^9 - 11183805/8*x^8
- 788238*x^7 - 98966*x^6 + 219224*x^5 + 199012*x^4 + 88800*x^3 + 23328*x^2 + 345
6*x

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Fricas [A]  time = 0.17848, size = 1, normalized size = 0.02 \[ -\frac{91125}{2} x^{12} - \frac{3262275}{11} x^{11} - \frac{1703673}{2} x^{10} - 1398447 x^{9} - \frac{11183805}{8} x^{8} - 788238 x^{7} - 98966 x^{6} + 219224 x^{5} + 199012 x^{4} + 88800 x^{3} + 23328 x^{2} + 3456 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^7*(2*x - 1),x, algorithm="fricas")

[Out]

-91125/2*x^12 - 3262275/11*x^11 - 1703673/2*x^10 - 1398447*x^9 - 11183805/8*x^8
- 788238*x^7 - 98966*x^6 + 219224*x^5 + 199012*x^4 + 88800*x^3 + 23328*x^2 + 345
6*x

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Sympy [A]  time = 0.120187, size = 65, normalized size = 1.16 \[ - \frac{91125 x^{12}}{2} - \frac{3262275 x^{11}}{11} - \frac{1703673 x^{10}}{2} - 1398447 x^{9} - \frac{11183805 x^{8}}{8} - 788238 x^{7} - 98966 x^{6} + 219224 x^{5} + 199012 x^{4} + 88800 x^{3} + 23328 x^{2} + 3456 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)*(2+3*x)**7*(3+5*x)**3,x)

[Out]

-91125*x**12/2 - 3262275*x**11/11 - 1703673*x**10/2 - 1398447*x**9 - 11183805*x*
*8/8 - 788238*x**7 - 98966*x**6 + 219224*x**5 + 199012*x**4 + 88800*x**3 + 23328
*x**2 + 3456*x

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GIAC/XCAS [A]  time = 0.204623, size = 80, normalized size = 1.43 \[ -\frac{91125}{2} \, x^{12} - \frac{3262275}{11} \, x^{11} - \frac{1703673}{2} \, x^{10} - 1398447 \, x^{9} - \frac{11183805}{8} \, x^{8} - 788238 \, x^{7} - 98966 \, x^{6} + 219224 \, x^{5} + 199012 \, x^{4} + 88800 \, x^{3} + 23328 \, x^{2} + 3456 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^3*(3*x + 2)^7*(2*x - 1),x, algorithm="giac")

[Out]

-91125/2*x^12 - 3262275/11*x^11 - 1703673/2*x^10 - 1398447*x^9 - 11183805/8*x^8
- 788238*x^7 - 98966*x^6 + 219224*x^5 + 199012*x^4 + 88800*x^3 + 23328*x^2 + 345
6*x