3.1.42 \(\int (8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4) \, dx\) [42]

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

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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 = {} \begin {gather*} 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 {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 37, normalized size = 1.00 \begin {gather*} 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 {gather*}

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 = 0.02, size = 34, normalized size = 0.92

method	result	size
gosper	\(8 a \,e^{2} x -\frac {1}{2} x^{2} d^{3}+2 x^{4} d \,e^{2}+\frac {8}{5} x^{5} e^{3}\)	\(34\)
default	\(8 a \,e^{2} x -\frac {1}{2} x^{2} d^{3}+2 x^{4} d \,e^{2}+\frac {8}{5} x^{5} e^{3}\)	\(34\)
norman	\(8 a \,e^{2} x -\frac {1}{2} x^{2} d^{3}+2 x^{4} d \,e^{2}+\frac {8}{5} x^{5} e^{3}\)	\(34\)
risch	\(8 a \,e^{2} x -\frac {1}{2} x^{2} d^{3}+2 x^{4} d \,e^{2}+\frac {8}{5} x^{5} e^{3}\)	\(34\)

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,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.26, size = 30, normalized size = 0.81 \begin {gather*} \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 {gather*}

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

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Fricas [A]
time = 0.37, size = 33, normalized size = 0.89 \begin {gather*} \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 {gather*}

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*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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Sympy [A]
time = 0.01, size = 36, normalized size = 0.97 \begin {gather*} 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 {gather*}

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 = 3.85, size = 30, normalized size = 0.81 \begin {gather*} \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 {gather*}

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

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

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

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