3.1163 \(\int (1-2 x) (2+3 x)^3 (3+5 x)^3 \, dx\)

Optimal. Leaf size=56 \[ -\frac{125}{972} (3 x+2)^8+\frac{1025 (3 x+2)^7}{1701}-\frac{185}{486} (3 x+2)^6+\frac{107 (3 x+2)^5}{1215}-\frac{7}{972} (3 x+2)^4 \]

[Out]

(-7*(2 + 3*x)^4)/972 + (107*(2 + 3*x)^5)/1215 - (185*(2 + 3*x)^6)/486 + (1025*(2
+ 3*x)^7)/1701 - (125*(2 + 3*x)^8)/972

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Rubi [A]  time = 0.0727846, 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 \[ -\frac{125}{972} (3 x+2)^8+\frac{1025 (3 x+2)^7}{1701}-\frac{185}{486} (3 x+2)^6+\frac{107 (3 x+2)^5}{1215}-\frac{7}{972} (3 x+2)^4 \]

Antiderivative was successfully verified.

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

[Out]

(-7*(2 + 3*x)^4)/972 + (107*(2 + 3*x)^5)/1215 - (185*(2 + 3*x)^6)/486 + (1025*(2
+ 3*x)^7)/1701 - (125*(2 + 3*x)^8)/972

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{3375 x^{8}}{4} - \frac{22275 x^{7}}{7} - \frac{9255 x^{6}}{2} - \frac{13943 x^{5}}{5} + \frac{883 x^{4}}{4} + 1338 x^{3} + 216 x + 1620 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375*x**8/4 - 22275*x**7/7 - 9255*x**6/2 - 13943*x**5/5 + 883*x**4/4 + 1338*x**
3 + 216*x + 1620*Integral(x, x)

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Mathematica [A]  time = 0.00218068, size = 49, normalized size = 0.88 \[ -\frac{3375 x^8}{4}-\frac{22275 x^7}{7}-\frac{9255 x^6}{2}-\frac{13943 x^5}{5}+\frac{883 x^4}{4}+1338 x^3+810 x^2+216 x \]

Antiderivative was successfully verified.

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

[Out]

216*x + 810*x^2 + 1338*x^3 + (883*x^4)/4 - (13943*x^5)/5 - (9255*x^6)/2 - (22275
*x^7)/7 - (3375*x^8)/4

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Maple [A]  time = 0., size = 40, normalized size = 0.7 \[ -{\frac{3375\,{x}^{8}}{4}}-{\frac{22275\,{x}^{7}}{7}}-{\frac{9255\,{x}^{6}}{2}}-{\frac{13943\,{x}^{5}}{5}}+{\frac{883\,{x}^{4}}{4}}+1338\,{x}^{3}+810\,{x}^{2}+216\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375/4*x^8-22275/7*x^7-9255/2*x^6-13943/5*x^5+883/4*x^4+1338*x^3+810*x^2+216*x

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Maxima [A]  time = 1.33718, size = 53, normalized size = 0.95 \[ -\frac{3375}{4} \, x^{8} - \frac{22275}{7} \, x^{7} - \frac{9255}{2} \, x^{6} - \frac{13943}{5} \, x^{5} + \frac{883}{4} \, x^{4} + 1338 \, x^{3} + 810 \, x^{2} + 216 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375/4*x^8 - 22275/7*x^7 - 9255/2*x^6 - 13943/5*x^5 + 883/4*x^4 + 1338*x^3 + 81
0*x^2 + 216*x

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Fricas [A]  time = 0.184701, size = 1, normalized size = 0.02 \[ -\frac{3375}{4} x^{8} - \frac{22275}{7} x^{7} - \frac{9255}{2} x^{6} - \frac{13943}{5} x^{5} + \frac{883}{4} x^{4} + 1338 x^{3} + 810 x^{2} + 216 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375/4*x^8 - 22275/7*x^7 - 9255/2*x^6 - 13943/5*x^5 + 883/4*x^4 + 1338*x^3 + 81
0*x^2 + 216*x

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Sympy [A]  time = 0.096722, size = 46, normalized size = 0.82 \[ - \frac{3375 x^{8}}{4} - \frac{22275 x^{7}}{7} - \frac{9255 x^{6}}{2} - \frac{13943 x^{5}}{5} + \frac{883 x^{4}}{4} + 1338 x^{3} + 810 x^{2} + 216 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375*x**8/4 - 22275*x**7/7 - 9255*x**6/2 - 13943*x**5/5 + 883*x**4/4 + 1338*x**
3 + 810*x**2 + 216*x

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GIAC/XCAS [A]  time = 0.205967, size = 53, normalized size = 0.95 \[ -\frac{3375}{4} \, x^{8} - \frac{22275}{7} \, x^{7} - \frac{9255}{2} \, x^{6} - \frac{13943}{5} \, x^{5} + \frac{883}{4} \, x^{4} + 1338 \, x^{3} + 810 \, x^{2} + 216 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375/4*x^8 - 22275/7*x^7 - 9255/2*x^6 - 13943/5*x^5 + 883/4*x^4 + 1338*x^3 + 81
0*x^2 + 216*x