3.1223 \(\int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx\)

Optimal. Leaf size=45 \[ \frac{5}{162} (3 x+2)^8-\frac{16}{63} (3 x+2)^7+\frac{91}{162} (3 x+2)^6-\frac{49}{405} (3 x+2)^5 \]

[Out]

(-49*(2 + 3*x)^5)/405 + (91*(2 + 3*x)^6)/162 - (16*(2 + 3*x)^7)/63 + (5*(2 + 3*x
)^8)/162

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Rubi [A]  time = 0.0699732, antiderivative size = 45, 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 \[ \frac{5}{162} (3 x+2)^8-\frac{16}{63} (3 x+2)^7+\frac{91}{162} (3 x+2)^6-\frac{49}{405} (3 x+2)^5 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x),x]

[Out]

(-49*(2 + 3*x)^5)/405 + (91*(2 + 3*x)^6)/162 - (16*(2 + 3*x)^7)/63 + (5*(2 + 3*x
)^8)/162

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{405 x^{8}}{2} + \frac{3672 x^{7}}{7} + \frac{675 x^{6}}{2} - \frac{1077 x^{5}}{5} - 328 x^{4} - \frac{152 x^{3}}{3} + 48 x + 176 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**2*(2+3*x)**4*(3+5*x),x)

[Out]

405*x**8/2 + 3672*x**7/7 + 675*x**6/2 - 1077*x**5/5 - 328*x**4 - 152*x**3/3 + 48
*x + 176*Integral(x, x)

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Mathematica [A]  time = 0.00195638, size = 49, normalized size = 1.09 \[ \frac{405 x^8}{2}+\frac{3672 x^7}{7}+\frac{675 x^6}{2}-\frac{1077 x^5}{5}-328 x^4-\frac{152 x^3}{3}+88 x^2+48 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^2*(2 + 3*x)^4*(3 + 5*x),x]

[Out]

48*x + 88*x^2 - (152*x^3)/3 - 328*x^4 - (1077*x^5)/5 + (675*x^6)/2 + (3672*x^7)/
7 + (405*x^8)/2

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Maple [A]  time = 0.002, size = 40, normalized size = 0.9 \[{\frac{405\,{x}^{8}}{2}}+{\frac{3672\,{x}^{7}}{7}}+{\frac{675\,{x}^{6}}{2}}-{\frac{1077\,{x}^{5}}{5}}-328\,{x}^{4}-{\frac{152\,{x}^{3}}{3}}+88\,{x}^{2}+48\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^2*(2+3*x)^4*(3+5*x),x)

[Out]

405/2*x^8+3672/7*x^7+675/2*x^6-1077/5*x^5-328*x^4-152/3*x^3+88*x^2+48*x

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Maxima [A]  time = 1.32633, size = 53, normalized size = 1.18 \[ \frac{405}{2} \, x^{8} + \frac{3672}{7} \, x^{7} + \frac{675}{2} \, x^{6} - \frac{1077}{5} \, x^{5} - 328 \, x^{4} - \frac{152}{3} \, x^{3} + 88 \, x^{2} + 48 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^4*(2*x - 1)^2,x, algorithm="maxima")

[Out]

405/2*x^8 + 3672/7*x^7 + 675/2*x^6 - 1077/5*x^5 - 328*x^4 - 152/3*x^3 + 88*x^2 +
48*x

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Fricas [A]  time = 0.183507, size = 1, normalized size = 0.02 \[ \frac{405}{2} x^{8} + \frac{3672}{7} x^{7} + \frac{675}{2} x^{6} - \frac{1077}{5} x^{5} - 328 x^{4} - \frac{152}{3} x^{3} + 88 x^{2} + 48 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^4*(2*x - 1)^2,x, algorithm="fricas")

[Out]

405/2*x^8 + 3672/7*x^7 + 675/2*x^6 - 1077/5*x^5 - 328*x^4 - 152/3*x^3 + 88*x^2 +
48*x

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Sympy [A]  time = 0.092082, size = 46, normalized size = 1.02 \[ \frac{405 x^{8}}{2} + \frac{3672 x^{7}}{7} + \frac{675 x^{6}}{2} - \frac{1077 x^{5}}{5} - 328 x^{4} - \frac{152 x^{3}}{3} + 88 x^{2} + 48 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**2*(2+3*x)**4*(3+5*x),x)

[Out]

405*x**8/2 + 3672*x**7/7 + 675*x**6/2 - 1077*x**5/5 - 328*x**4 - 152*x**3/3 + 88
*x**2 + 48*x

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GIAC/XCAS [A]  time = 0.205131, size = 53, normalized size = 1.18 \[ \frac{405}{2} \, x^{8} + \frac{3672}{7} \, x^{7} + \frac{675}{2} \, x^{6} - \frac{1077}{5} \, x^{5} - 328 \, x^{4} - \frac{152}{3} \, x^{3} + 88 \, x^{2} + 48 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)*(3*x + 2)^4*(2*x - 1)^2,x, algorithm="giac")

[Out]

405/2*x^8 + 3672/7*x^7 + 675/2*x^6 - 1077/5*x^5 - 328*x^4 - 152/3*x^3 + 88*x^2 +
48*x