3.90.41 \(\int \frac {9 e^2 x}{2} \, dx\)

Optimal. Leaf size=12 \[ -3+\frac {9 e^2 x^2}{4} \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.83, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \begin {gather*} \frac {9 e^2 x^2}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(9*E^2*x)/2,x]

[Out]

(9*E^2*x^2)/4

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \left (9 e^2\right ) \int x \, dx\\ &=\frac {9 e^2 x^2}{4}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} \frac {9 e^2 x^2}{4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(9*E^2*x)/2,x]

[Out]

(9*E^2*x^2)/4

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fricas [A]  time = 0.65, size = 7, normalized size = 0.58 \begin {gather*} \frac {9}{4} \, x^{2} e^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9/2*exp(2)*x,x, algorithm="fricas")

[Out]

9/4*x^2*e^2

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giac [A]  time = 0.20, size = 7, normalized size = 0.58 \begin {gather*} \frac {9}{4} \, x^{2} e^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9/2*exp(2)*x,x, algorithm="giac")

[Out]

9/4*x^2*e^2

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maple [A]  time = 0.02, size = 8, normalized size = 0.67

method	result	size
gosper	\(\frac {9 x^{2} {\mathrm e}^{2}}{4}\)	\(8\)
default	\(\frac {9 x^{2} {\mathrm e}^{2}}{4}\)	\(8\)
norman	\(\frac {9 x^{2} {\mathrm e}^{2}}{4}\)	\(8\)
risch	\(\frac {9 x^{2} {\mathrm e}^{2}}{4}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(9/2*exp(2)*x,x,method=_RETURNVERBOSE)

[Out]

9/4*x^2*exp(2)

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maxima [A]  time = 0.34, size = 7, normalized size = 0.58 \begin {gather*} \frac {9}{4} \, x^{2} e^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9/2*exp(2)*x,x, algorithm="maxima")

[Out]

9/4*x^2*e^2

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mupad [B]  time = 0.05, size = 7, normalized size = 0.58 \begin {gather*} \frac {9\,x^2\,{\mathrm {e}}^2}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((9*x*exp(2))/2,x)

[Out]

(9*x^2*exp(2))/4

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sympy [A]  time = 0.02, size = 8, normalized size = 0.67 \begin {gather*} \frac {9 x^{2} e^{2}}{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(9/2*exp(2)*x,x)

[Out]

9*x**2*exp(2)/4

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