3.42 \(\int (8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4) \, dx\)

Optimal. Leaf size=37 \[ 8 a e^2 x-\frac{d^3 x^2}{2}+2 d e^2 x^4+\frac{8 e^3 x^5}{5} \]

[Out]

8*a*e^2*x - (d^3*x^2)/2 + 2*d*e^2*x^4 + (8*e^3*x^5)/5

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Rubi [A]  time = 0.0073737, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ 8 a e^2 x-\frac{d^3 x^2}{2}+2 d e^2 x^4+\frac{8 e^3 x^5}{5} \]

Antiderivative was successfully verified.

[In]

Int[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4,x]

[Out]

8*a*e^2*x - (d^3*x^2)/2 + 2*d*e^2*x^4 + (8*e^3*x^5)/5

Rubi steps

\begin{align*} \int \left (8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right ) \, dx &=8 a e^2 x-\frac{d^3 x^2}{2}+2 d e^2 x^4+\frac{8 e^3 x^5}{5}\\ \end{align*}

Mathematica [A]  time = 0.0000512, size = 37, normalized size = 1. \[ 8 a e^2 x-\frac{d^3 x^2}{2}+2 d e^2 x^4+\frac{8 e^3 x^5}{5} \]

Antiderivative was successfully verified.

[In]

Integrate[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4,x]

[Out]

8*a*e^2*x - (d^3*x^2)/2 + 2*d*e^2*x^4 + (8*e^3*x^5)/5

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Maple [A]  time = 0., size = 34, normalized size = 0.9 \begin{align*} 8\,a{e}^{2}x-{\frac{{d}^{3}{x}^{2}}{2}}+2\,d{e}^{2}{x}^{4}+{\frac{8\,{e}^{3}{x}^{5}}{5}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2,x)

[Out]

8*a*e^2*x-1/2*d^3*x^2+2*d*e^2*x^4+8/5*e^3*x^5

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Maxima [A]  time = 1.15237, size = 45, normalized size = 1.22 \begin{align*} \frac{8}{5} \, e^{3} x^{5} + 2 \, d e^{2} x^{4} - \frac{1}{2} \, d^{3} x^{2} + 8 \, a e^{2} x \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2,x, algorithm="maxima")

[Out]

8/5*e^3*x^5 + 2*d*e^2*x^4 - 1/2*d^3*x^2 + 8*a*e^2*x

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Fricas [A]  time = 1.26313, size = 72, normalized size = 1.95 \begin{align*} \frac{8}{5} x^{5} e^{3} + 2 x^{4} e^{2} d - \frac{1}{2} x^{2} d^{3} + 8 x e^{2} a \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2,x, algorithm="fricas")

[Out]

8/5*x^5*e^3 + 2*x^4*e^2*d - 1/2*x^2*d^3 + 8*x*e^2*a

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Sympy [A]  time = 0.06298, size = 36, normalized size = 0.97 \begin{align*} 8 a e^{2} x - \frac{d^{3} x^{2}}{2} + 2 d e^{2} x^{4} + \frac{8 e^{3} x^{5}}{5} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*e**3*x**4+8*d*e**2*x**3-d**3*x+8*a*e**2,x)

[Out]

8*a*e**2*x - d**3*x**2/2 + 2*d*e**2*x**4 + 8*e**3*x**5/5

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Giac [A]  time = 1.14496, size = 41, normalized size = 1.11 \begin{align*} \frac{8}{5} \, x^{5} e^{3} + 2 \, d x^{4} e^{2} - \frac{1}{2} \, d^{3} x^{2} + 8 \, a x e^{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2,x, algorithm="giac")

[Out]

8/5*x^5*e^3 + 2*d*x^4*e^2 - 1/2*d^3*x^2 + 8*a*x*e^2