3.72.97 \(\int (10 x-3 x^2+e^{2 e^{9 x^2}} (2 x+36 e^{9 x^2} x^3)) \, dx\)

Optimal. Leaf size=20 \[ \left (5+e^{2 e^{9 x^2}}-x\right ) x^2 \]

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Rubi [A]  time = 0.03, antiderivative size = 26, normalized size of antiderivative = 1.30, number of steps used = 2, number of rules used = 1, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {2288} \begin {gather*} -x^3+e^{2 e^{9 x^2}} x^2+5 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[10*x - 3*x^2 + E^(2*E^(9*x^2))*(2*x + 36*E^(9*x^2)*x^3),x]

[Out]

5*x^2 + E^(2*E^(9*x^2))*x^2 - x^3

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=5 x^2-x^3+\int e^{2 e^{9 x^2}} \left (2 x+36 e^{9 x^2} x^3\right ) \, dx\\ &=5 x^2+e^{2 e^{9 x^2}} x^2-x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.04, size = 21, normalized size = 1.05 \begin {gather*} -x^2 \left (-5-e^{2 e^{9 x^2}}+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[10*x - 3*x^2 + E^(2*E^(9*x^2))*(2*x + 36*E^(9*x^2)*x^3),x]

[Out]

-(x^2*(-5 - E^(2*E^(9*x^2)) + x))

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fricas [A]  time = 0.78, size = 24, normalized size = 1.20 \begin {gather*} -x^{3} + x^{2} e^{\left (2 \, e^{\left (9 \, x^{2}\right )}\right )} + 5 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x^3*exp(9*x^2)+2*x)*exp(exp(9*x^2))^2-3*x^2+10*x,x, algorithm="fricas")

[Out]

-x^3 + x^2*e^(2*e^(9*x^2)) + 5*x^2

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -3 \, x^{2} + 2 \, {\left (18 \, x^{3} e^{\left (9 \, x^{2}\right )} + x\right )} e^{\left (2 \, e^{\left (9 \, x^{2}\right )}\right )} + 10 \, x\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x^3*exp(9*x^2)+2*x)*exp(exp(9*x^2))^2-3*x^2+10*x,x, algorithm="giac")

[Out]

integrate(-3*x^2 + 2*(18*x^3*e^(9*x^2) + x)*e^(2*e^(9*x^2)) + 10*x, x)

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maple [A]  time = 0.06, size = 25, normalized size = 1.25

method	result	size
default	\(x^{2} {\mathrm e}^{2 \,{\mathrm e}^{9 x^{2}}}+5 x^{2}-x^{3}\)	\(25\)
norman	\(x^{2} {\mathrm e}^{2 \,{\mathrm e}^{9 x^{2}}}+5 x^{2}-x^{3}\)	\(25\)
risch	\(x^{2} {\mathrm e}^{2 \,{\mathrm e}^{9 x^{2}}}+5 x^{2}-x^{3}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((36*x^3*exp(9*x^2)+2*x)*exp(exp(9*x^2))^2-3*x^2+10*x,x,method=_RETURNVERBOSE)

[Out]

x^2*exp(exp(9*x^2))^2+5*x^2-x^3

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maxima [A]  time = 0.35, size = 24, normalized size = 1.20 \begin {gather*} -x^{3} + x^{2} e^{\left (2 \, e^{\left (9 \, x^{2}\right )}\right )} + 5 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x^3*exp(9*x^2)+2*x)*exp(exp(9*x^2))^2-3*x^2+10*x,x, algorithm="maxima")

[Out]

-x^3 + x^2*e^(2*e^(9*x^2)) + 5*x^2

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mupad [B]  time = 4.29, size = 18, normalized size = 0.90 \begin {gather*} x^2\,\left ({\mathrm {e}}^{2\,{\mathrm {e}}^{9\,x^2}}-x+5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*x + exp(2*exp(9*x^2))*(2*x + 36*x^3*exp(9*x^2)) - 3*x^2,x)

[Out]

x^2*(exp(2*exp(9*x^2)) - x + 5)

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sympy [A]  time = 0.32, size = 20, normalized size = 1.00 \begin {gather*} - x^{3} + x^{2} e^{2 e^{9 x^{2}}} + 5 x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((36*x**3*exp(9*x**2)+2*x)*exp(exp(9*x**2))**2-3*x**2+10*x,x)

[Out]

-x**3 + x**2*exp(2*exp(9*x**2)) + 5*x**2

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