3.656 \(\int e^{3 x} \left (-8+2 x^3+x^5\right ) \, dx\)

Optimal. Leaf size=68 \[ \frac{1}{3} e^{3 x} x^5-\frac{5}{9} e^{3 x} x^4+\frac{38}{27} e^{3 x} x^3-\frac{38}{27} e^{3 x} x^2+\frac{76}{81} e^{3 x} x-\frac{724 e^{3 x}}{243} \]

[Out]

(-724*E^(3*x))/243 + (76*E^(3*x)*x)/81 - (38*E^(3*x)*x^2)/27 + (38*E^(3*x)*x^3)/
27 - (5*E^(3*x)*x^4)/9 + (E^(3*x)*x^5)/3

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Rubi [A]  time = 0.16355, antiderivative size = 68, normalized size of antiderivative = 1., number of steps used = 13, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188 \[ \frac{1}{3} e^{3 x} x^5-\frac{5}{9} e^{3 x} x^4+\frac{38}{27} e^{3 x} x^3-\frac{38}{27} e^{3 x} x^2+\frac{76}{81} e^{3 x} x-\frac{724 e^{3 x}}{243} \]

Antiderivative was successfully verified.

[In]  Int[E^(3*x)*(-8 + 2*x^3 + x^5),x]

[Out]

(-724*E^(3*x))/243 + (76*E^(3*x)*x)/81 - (38*E^(3*x)*x^2)/27 + (38*E^(3*x)*x^3)/
27 - (5*E^(3*x)*x^4)/9 + (E^(3*x)*x^5)/3

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Rubi in Sympy [A]  time = 13.0511, size = 63, normalized size = 0.93 \[ \frac{x^{5} e^{3 x}}{3} - \frac{5 x^{4} e^{3 x}}{9} + \frac{38 x^{3} e^{3 x}}{27} - \frac{38 x^{2} e^{3 x}}{27} + \frac{76 x e^{3 x}}{81} - \frac{724 e^{3 x}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(3*x)*(x**5+2*x**3-8),x)

[Out]

x**5*exp(3*x)/3 - 5*x**4*exp(3*x)/9 + 38*x**3*exp(3*x)/27 - 38*x**2*exp(3*x)/27
+ 76*x*exp(3*x)/81 - 724*exp(3*x)/243

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Mathematica [A]  time = 0.00824244, size = 34, normalized size = 0.5 \[ \frac{1}{243} e^{3 x} \left (81 x^5-135 x^4+342 x^3-342 x^2+228 x-724\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[E^(3*x)*(-8 + 2*x^3 + x^5),x]

[Out]

(E^(3*x)*(-724 + 228*x - 342*x^2 + 342*x^3 - 135*x^4 + 81*x^5))/243

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Maple [A]  time = 0.009, size = 32, normalized size = 0.5 \[{\frac{{{\rm e}^{3\,x}} \left ( 81\,{x}^{5}-135\,{x}^{4}+342\,{x}^{3}-342\,{x}^{2}+228\,x-724 \right ) }{243}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(3*x)*(x^5+2*x^3-8),x)

[Out]

1/243*exp(3*x)*(81*x^5-135*x^4+342*x^3-342*x^2+228*x-724)

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Maxima [A]  time = 0.784615, size = 80, normalized size = 1.18 \[ \frac{1}{243} \,{\left (81 \, x^{5} - 135 \, x^{4} + 180 \, x^{3} - 180 \, x^{2} + 120 \, x - 40\right )} e^{\left (3 \, x\right )} + \frac{2}{27} \,{\left (9 \, x^{3} - 9 \, x^{2} + 6 \, x - 2\right )} e^{\left (3 \, x\right )} - \frac{8}{3} \, e^{\left (3 \, x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^5 + 2*x^3 - 8)*e^(3*x),x, algorithm="maxima")

[Out]

1/243*(81*x^5 - 135*x^4 + 180*x^3 - 180*x^2 + 120*x - 40)*e^(3*x) + 2/27*(9*x^3
- 9*x^2 + 6*x - 2)*e^(3*x) - 8/3*e^(3*x)

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Fricas [A]  time = 0.222788, size = 42, normalized size = 0.62 \[ \frac{1}{243} \,{\left (81 \, x^{5} - 135 \, x^{4} + 342 \, x^{3} - 342 \, x^{2} + 228 \, x - 724\right )} e^{\left (3 \, x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^5 + 2*x^3 - 8)*e^(3*x),x, algorithm="fricas")

[Out]

1/243*(81*x^5 - 135*x^4 + 342*x^3 - 342*x^2 + 228*x - 724)*e^(3*x)

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Sympy [A]  time = 0.083765, size = 31, normalized size = 0.46 \[ \frac{\left (81 x^{5} - 135 x^{4} + 342 x^{3} - 342 x^{2} + 228 x - 724\right ) e^{3 x}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(3*x)*(x**5+2*x**3-8),x)

[Out]

(81*x**5 - 135*x**4 + 342*x**3 - 342*x**2 + 228*x - 724)*exp(3*x)/243

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GIAC/XCAS [A]  time = 0.259901, size = 42, normalized size = 0.62 \[ \frac{1}{243} \,{\left (81 \, x^{5} - 135 \, x^{4} + 342 \, x^{3} - 342 \, x^{2} + 228 \, x - 724\right )} e^{\left (3 \, x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^5 + 2*x^3 - 8)*e^(3*x),x, algorithm="giac")

[Out]

1/243*(81*x^5 - 135*x^4 + 342*x^3 - 342*x^2 + 228*x - 724)*e^(3*x)