3.1261 \(\int (1-2 x)^2 (2+3 x)^2 (3+5 x)^3 \, dx\)

Optimal. Leaf size=56 \[ \frac{9 (5 x+3)^8}{6250}-\frac{372 (5 x+3)^7}{21875}+\frac{829 (5 x+3)^6}{18750}+\frac{682 (5 x+3)^5}{15625}+\frac{121 (5 x+3)^4}{12500} \]

[Out]

(121*(3 + 5*x)^4)/12500 + (682*(3 + 5*x)^5)/15625 + (829*(3 + 5*x)^6)/18750 - (3
72*(3 + 5*x)^7)/21875 + (9*(3 + 5*x)^8)/6250

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Rubi [A]  time = 0.0838589, antiderivative size = 56, 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 \[ \frac{9 (5 x+3)^8}{6250}-\frac{372 (5 x+3)^7}{21875}+\frac{829 (5 x+3)^6}{18750}+\frac{682 (5 x+3)^5}{15625}+\frac{121 (5 x+3)^4}{12500} \]

Antiderivative was successfully verified.

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

[Out]

(121*(3 + 5*x)^4)/12500 + (682*(3 + 5*x)^5)/15625 + (829*(3 + 5*x)^6)/18750 - (3
72*(3 + 5*x)^7)/21875 + (9*(3 + 5*x)^8)/6250

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{1125 x^{8}}{2} + \frac{9600 x^{7}}{7} + \frac{4685 x^{6}}{6} - \frac{3083 x^{5}}{5} - \frac{3181 x^{4}}{4} - 87 x^{3} + 108 x + 432 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125*x**8/2 + 9600*x**7/7 + 4685*x**6/6 - 3083*x**5/5 - 3181*x**4/4 - 87*x**3 +
108*x + 432*Integral(x, x)

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Mathematica [A]  time = 0.00396843, size = 49, normalized size = 0.88 \[ \frac{1125 x^8}{2}+\frac{9600 x^7}{7}+\frac{4685 x^6}{6}-\frac{3083 x^5}{5}-\frac{3181 x^4}{4}-87 x^3+216 x^2+108 x \]

Antiderivative was successfully verified.

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

[Out]

108*x + 216*x^2 - 87*x^3 - (3181*x^4)/4 - (3083*x^5)/5 + (4685*x^6)/6 + (9600*x^
7)/7 + (1125*x^8)/2

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Maple [A]  time = 0.002, size = 40, normalized size = 0.7 \[{\frac{1125\,{x}^{8}}{2}}+{\frac{9600\,{x}^{7}}{7}}+{\frac{4685\,{x}^{6}}{6}}-{\frac{3083\,{x}^{5}}{5}}-{\frac{3181\,{x}^{4}}{4}}-87\,{x}^{3}+216\,{x}^{2}+108\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125/2*x^8+9600/7*x^7+4685/6*x^6-3083/5*x^5-3181/4*x^4-87*x^3+216*x^2+108*x

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Maxima [A]  time = 1.32801, size = 53, normalized size = 0.95 \[ \frac{1125}{2} \, x^{8} + \frac{9600}{7} \, x^{7} + \frac{4685}{6} \, x^{6} - \frac{3083}{5} \, x^{5} - \frac{3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^
2 + 108*x

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Fricas [A]  time = 0.186641, size = 1, normalized size = 0.02 \[ \frac{1125}{2} x^{8} + \frac{9600}{7} x^{7} + \frac{4685}{6} x^{6} - \frac{3083}{5} x^{5} - \frac{3181}{4} x^{4} - 87 x^{3} + 216 x^{2} + 108 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^
2 + 108*x

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Sympy [A]  time = 0.095328, size = 46, normalized size = 0.82 \[ \frac{1125 x^{8}}{2} + \frac{9600 x^{7}}{7} + \frac{4685 x^{6}}{6} - \frac{3083 x^{5}}{5} - \frac{3181 x^{4}}{4} - 87 x^{3} + 216 x^{2} + 108 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125*x**8/2 + 9600*x**7/7 + 4685*x**6/6 - 3083*x**5/5 - 3181*x**4/4 - 87*x**3 +
216*x**2 + 108*x

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GIAC/XCAS [A]  time = 0.212383, size = 53, normalized size = 0.95 \[ \frac{1125}{2} \, x^{8} + \frac{9600}{7} \, x^{7} + \frac{4685}{6} \, x^{6} - \frac{3083}{5} \, x^{5} - \frac{3181}{4} \, x^{4} - 87 \, x^{3} + 216 \, x^{2} + 108 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1125/2*x^8 + 9600/7*x^7 + 4685/6*x^6 - 3083/5*x^5 - 3181/4*x^4 - 87*x^3 + 216*x^
2 + 108*x