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

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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 = 0.00, size = 37, normalized size = 1.00 \[ 8 a e^2 x-\frac {d^3 x^2}{2}+2 d e^2 x^4+\frac {8 e^3 x^5}{5} \]

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

________________________________________________________________________________________

fricas [A]  time = 0.38, size = 33, normalized size = 0.89 \[ \frac {8}{5} x^{5} e^{3} + 2 x^{4} e^{2} d - \frac {1}{2} x^{2} d^{3} + 8 x e^{2} a \]

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

________________________________________________________________________________________

giac [A]  time = 0.38, size = 30, normalized size = 0.81 \[ \frac {8}{5} \, x^{5} e^{3} + 2 \, d x^{4} e^{2} - \frac {1}{2} \, d^{3} x^{2} + 8 \, a x e^{2} \]

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

________________________________________________________________________________________

maple [A]  time = 0.00, size = 34, normalized size = 0.92 \[ \frac {8}{5} e^{3} x^{5}+2 d \,e^{2} x^{4}-\frac {1}{2} d^{3} x^{2}+8 a \,e^{2} x \]

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

________________________________________________________________________________________

maxima [A]  time = 0.67, size = 33, normalized size = 0.89 \[ \frac {8}{5} \, e^{3} x^{5} + 2 \, d e^{2} x^{4} - \frac {1}{2} \, d^{3} x^{2} + 8 \, a e^{2} x \]

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

________________________________________________________________________________________

mupad [B]  time = 0.04, size = 33, normalized size = 0.89 \[ -\frac {d^3\,x^2}{2}+2\,d\,e^2\,x^4+\frac {8\,e^3\,x^5}{5}+8\,a\,e^2\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 0.07, size = 36, normalized size = 0.97 \[ 8 a e^{2} x - \frac {d^{3} x^{2}}{2} + 2 d e^{2} x^{4} + \frac {8 e^{3} x^{5}}{5} \]

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

________________________________________________________________________________________