3.46.14 \(\int \frac {1}{6} (9 x^2+18 e^4 x^2+24 x^3-22 x^{10}) \, dx\)

Optimal. Leaf size=19 \[ x^3 \left (\frac {1}{2}+e^4+x-\frac {x^8}{3}\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.32, number of steps used = 3, number of rules used = 2, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {6, 12} \begin {gather*} -\frac {x^{11}}{3}+x^4+\frac {1}{2} \left (1+2 e^4\right ) x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(9*x^2 + 18*E^4*x^2 + 24*x^3 - 22*x^10)/6,x]

[Out]

((1 + 2*E^4)*x^3)/2 + x^4 - x^11/3

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

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} &=\int \frac {1}{6} \left (\left (9+18 e^4\right ) x^2+24 x^3-22 x^{10}\right ) \, dx\\ &=\frac {1}{6} \int \left (\left (9+18 e^4\right ) x^2+24 x^3-22 x^{10}\right ) \, dx\\ &=\frac {1}{2} \left (1+2 e^4\right ) x^3+x^4-\frac {x^{11}}{3}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 22, normalized size = 1.16 \begin {gather*} \frac {1}{6} x^3 \left (3+6 e^4+6 x-2 x^8\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(9*x^2 + 18*E^4*x^2 + 24*x^3 - 22*x^10)/6,x]

[Out]

(x^3*(3 + 6*E^4 + 6*x - 2*x^8))/6

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fricas [A]  time = 0.69, size = 20, normalized size = 1.05 \begin {gather*} -\frac {1}{3} \, x^{11} + x^{4} + x^{3} e^{4} + \frac {1}{2} \, x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2*exp(4)-11/3*x^10+4*x^3+3/2*x^2,x, algorithm="fricas")

[Out]

-1/3*x^11 + x^4 + x^3*e^4 + 1/2*x^3

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giac [A]  time = 0.16, size = 20, normalized size = 1.05 \begin {gather*} -\frac {1}{3} \, x^{11} + x^{4} + x^{3} e^{4} + \frac {1}{2} \, x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2*exp(4)-11/3*x^10+4*x^3+3/2*x^2,x, algorithm="giac")

[Out]

-1/3*x^11 + x^4 + x^3*e^4 + 1/2*x^3

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maple [A]  time = 0.03, size = 18, normalized size = 0.95

method	result	size
norman	\(x^{4}+\left ({\mathrm e}^{4}+\frac {1}{2}\right ) x^{3}-\frac {x^{11}}{3}\)	\(18\)
gosper	\(\frac {x^{3} \left (-2 x^{8}+6 \,{\mathrm e}^{4}+6 x +3\right )}{6}\)	\(20\)
default	\(x^{3} {\mathrm e}^{4}-\frac {x^{11}}{3}+x^{4}+\frac {x^{3}}{2}\)	\(21\)
risch	\(x^{3} {\mathrm e}^{4}-\frac {x^{11}}{3}+x^{4}+\frac {x^{3}}{2}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2*exp(4)-11/3*x^10+4*x^3+3/2*x^2,x,method=_RETURNVERBOSE)

[Out]

x^4+(exp(4)+1/2)*x^3-1/3*x^11

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maxima [A]  time = 0.36, size = 20, normalized size = 1.05 \begin {gather*} -\frac {1}{3} \, x^{11} + x^{4} + x^{3} e^{4} + \frac {1}{2} \, x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x^2*exp(4)-11/3*x^10+4*x^3+3/2*x^2,x, algorithm="maxima")

[Out]

-1/3*x^11 + x^4 + x^3*e^4 + 1/2*x^3

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mupad [B]  time = 3.16, size = 17, normalized size = 0.89 \begin {gather*} -\frac {x^{11}}{3}+x^4+\left ({\mathrm {e}}^4+\frac {1}{2}\right )\,x^3 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2*exp(4) + (3*x^2)/2 + 4*x^3 - (11*x^10)/3,x)

[Out]

x^4 - x^11/3 + x^3*(exp(4) + 1/2)

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sympy [A]  time = 0.06, size = 17, normalized size = 0.89 \begin {gather*} - \frac {x^{11}}{3} + x^{4} + x^{3} \left (\frac {1}{2} + e^{4}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x**2*exp(4)-11/3*x**10+4*x**3+3/2*x**2,x)

[Out]

-x**11/3 + x**4 + x**3*(1/2 + exp(4))

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