3.70.51 \(\int \frac {1}{2} (3+2 e^5+6 x^2) \, dx\)

Optimal. Leaf size=23 \[ -6-e+x+e^5 x+x^3+\frac {1}{4} (1+2 x) \]

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.70, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12} \begin {gather*} x^3+\frac {1}{2} \left (3+2 e^5\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(3 + 2*E^5 + 6*x^2)/2,x]

[Out]

((3 + 2*E^5)*x)/2 + x^3

Rule 12

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (3+2 e^5+6 x^2\right ) \, dx\\ &=\frac {1}{2} \left (3+2 e^5\right ) x+x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.61 \begin {gather*} \frac {3 x}{2}+e^5 x+x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3 + 2*E^5 + 6*x^2)/2,x]

[Out]

(3*x)/2 + E^5*x + x^3

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fricas [A]  time = 0.65, size = 11, normalized size = 0.48 \begin {gather*} x^{3} + x e^{5} + \frac {3}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(5)+3*x^2+3/2,x, algorithm="fricas")

[Out]

x^3 + x*e^5 + 3/2*x

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giac [A]  time = 0.21, size = 11, normalized size = 0.48 \begin {gather*} x^{3} + x e^{5} + \frac {3}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(5)+3*x^2+3/2,x, algorithm="giac")

[Out]

x^3 + x*e^5 + 3/2*x

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maple [A]  time = 0.02, size = 11, normalized size = 0.48

method	result	size
norman	\(x^{3}+\left ({\mathrm e}^{5}+\frac {3}{2}\right ) x\)	\(11\)
default	\(x \,{\mathrm e}^{5}+x^{3}+\frac {3 x}{2}\)	\(12\)
risch	\(x \,{\mathrm e}^{5}+x^{3}+\frac {3 x}{2}\)	\(12\)
gosper	\(\frac {x \left (2 x^{2}+2 \,{\mathrm e}^{5}+3\right )}{2}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(5)+3*x^2+3/2,x,method=_RETURNVERBOSE)

[Out]

x^3+(exp(5)+3/2)*x

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maxima [A]  time = 0.37, size = 11, normalized size = 0.48 \begin {gather*} x^{3} + x e^{5} + \frac {3}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(5)+3*x^2+3/2,x, algorithm="maxima")

[Out]

x^3 + x*e^5 + 3/2*x

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mupad [B]  time = 0.02, size = 10, normalized size = 0.43 \begin {gather*} x^3+\left ({\mathrm {e}}^5+\frac {3}{2}\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(5) + 3*x^2 + 3/2,x)

[Out]

x*(exp(5) + 3/2) + x^3

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sympy [A]  time = 0.05, size = 10, normalized size = 0.43 \begin {gather*} x^{3} + x \left (\frac {3}{2} + e^{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(5)+3*x**2+3/2,x)

[Out]

x**3 + x*(3/2 + exp(5))

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