3.1164 \(\int (1-2 x) (2+3 x)^2 (3+5 x)^3 \, dx\)

Optimal. Leaf size=45 \[ -\frac{18 (5 x+3)^7}{4375}+\frac{29 (5 x+3)^6}{1250}+\frac{64 (5 x+3)^5}{3125}+\frac{11 (5 x+3)^4}{2500} \]

[Out]

(11*(3 + 5*x)^4)/2500 + (64*(3 + 5*x)^5)/3125 + (29*(3 + 5*x)^6)/1250 - (18*(3 +
5*x)^7)/4375

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Rubi [A]  time = 0.0631541, 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 \[ -\frac{18 (5 x+3)^7}{4375}+\frac{29 (5 x+3)^6}{1250}+\frac{64 (5 x+3)^5}{3125}+\frac{11 (5 x+3)^4}{2500} \]

Antiderivative was successfully verified.

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

[Out]

(11*(3 + 5*x)^4)/2500 + (64*(3 + 5*x)^5)/3125 + (29*(3 + 5*x)^6)/1250 - (18*(3 +
5*x)^7)/4375

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{2250 x^{7}}{7} - \frac{1975 x^{6}}{2} - 1061 x^{5} - \frac{1111 x^{4}}{4} + 345 x^{3} + 108 x + 648 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2250*x**7/7 - 1975*x**6/2 - 1061*x**5 - 1111*x**4/4 + 345*x**3 + 108*x + 648*In
tegral(x, x)

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Mathematica [A]  time = 0.00163991, size = 40, normalized size = 0.89 \[ -\frac{2250 x^7}{7}-\frac{1975 x^6}{2}-1061 x^5-\frac{1111 x^4}{4}+345 x^3+324 x^2+108 x \]

Antiderivative was successfully verified.

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

[Out]

108*x + 324*x^2 + 345*x^3 - (1111*x^4)/4 - 1061*x^5 - (1975*x^6)/2 - (2250*x^7)/
7

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Maple [A]  time = 0.003, size = 35, normalized size = 0.8 \[ -{\frac{2250\,{x}^{7}}{7}}-{\frac{1975\,{x}^{6}}{2}}-1061\,{x}^{5}-{\frac{1111\,{x}^{4}}{4}}+345\,{x}^{3}+324\,{x}^{2}+108\,x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2250/7*x^7-1975/2*x^6-1061*x^5-1111/4*x^4+345*x^3+324*x^2+108*x

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Maxima [A]  time = 1.34896, size = 46, normalized size = 1.02 \[ -\frac{2250}{7} \, x^{7} - \frac{1975}{2} \, x^{6} - 1061 \, x^{5} - \frac{1111}{4} \, x^{4} + 345 \, x^{3} + 324 \, x^{2} + 108 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2250/7*x^7 - 1975/2*x^6 - 1061*x^5 - 1111/4*x^4 + 345*x^3 + 324*x^2 + 108*x

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Fricas [A]  time = 0.187085, size = 1, normalized size = 0.02 \[ -\frac{2250}{7} x^{7} - \frac{1975}{2} x^{6} - 1061 x^{5} - \frac{1111}{4} x^{4} + 345 x^{3} + 324 x^{2} + 108 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2250/7*x^7 - 1975/2*x^6 - 1061*x^5 - 1111/4*x^4 + 345*x^3 + 324*x^2 + 108*x

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Sympy [A]  time = 0.084344, size = 37, normalized size = 0.82 \[ - \frac{2250 x^{7}}{7} - \frac{1975 x^{6}}{2} - 1061 x^{5} - \frac{1111 x^{4}}{4} + 345 x^{3} + 324 x^{2} + 108 x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2250*x**7/7 - 1975*x**6/2 - 1061*x**5 - 1111*x**4/4 + 345*x**3 + 324*x**2 + 108
*x

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GIAC/XCAS [A]  time = 0.208869, size = 46, normalized size = 1.02 \[ -\frac{2250}{7} \, x^{7} - \frac{1975}{2} \, x^{6} - 1061 \, x^{5} - \frac{1111}{4} \, x^{4} + 345 \, x^{3} + 324 \, x^{2} + 108 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2250/7*x^7 - 1975/2*x^6 - 1061*x^5 - 1111/4*x^4 + 345*x^3 + 324*x^2 + 108*x