\(\int (10 x-3 x^2+e^{2 e^{9 x^2}} (2 x+36 e^{9 x^2} x^3)) \, dx\) [7197]

Optimal result

Integrand size = 37, antiderivative size = 20 \[ \int \left (10 x-3 x^2+e^{2 e^{9 x^2}} \left (2 x+36 e^{9 x^2} x^3\right )\right ) \, dx=\left (5+e^{2 e^{9 x^2}}-x\right ) x^2 \]

[Out]

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

Rubi [A] (verified)

Time = 0.02 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.30, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {2326} \[ \int \left (10 x-3 x^2+e^{2 e^{9 x^2}} \left (2 x+36 e^{9 x^2} x^3\right )\right ) \, dx=-x^3+e^{2 e^{9 x^2}} x^2+5 x^2 \]

[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 2326

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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.04 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int \left (10 x-3 x^2+e^{2 e^{9 x^2}} \left (2 x+36 e^{9 x^2} x^3\right )\right ) \, dx=-x^2 \left (-5-e^{2 e^{9 x^2}}+x\right ) \]

[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))

Maple [A] (verified)

Time = 0.15 (sec) , antiderivative size = 25, normalized size of antiderivative = 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	\(x^{2} {\mathrm e}^{2 \,{\mathrm e}^{9 x^{2}}}+5 x^{2}-x^{3}\)	\(25\)
parallelrisch	\(x^{2} {\mathrm e}^{2 \,{\mathrm e}^{9 x^{2}}}+5 x^{2}-x^{3}\)	\(25\)

[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

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \left (10 x-3 x^2+e^{2 e^{9 x^2}} \left (2 x+36 e^{9 x^2} x^3\right )\right ) \, dx=-x^{3} + x^{2} e^{\left (2 \, e^{\left (9 \, x^{2}\right )}\right )} + 5 \, x^{2} \]

[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

Sympy [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \left (10 x-3 x^2+e^{2 e^{9 x^2}} \left (2 x+36 e^{9 x^2} x^3\right )\right ) \, dx=- x^{3} + x^{2} e^{2 e^{9 x^{2}}} + 5 x^{2} \]

[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

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.20 \[ \int \left (10 x-3 x^2+e^{2 e^{9 x^2}} \left (2 x+36 e^{9 x^2} x^3\right )\right ) \, dx=-x^{3} + x^{2} e^{\left (2 \, e^{\left (9 \, x^{2}\right )}\right )} + 5 \, x^{2} \]

[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

Giac [F]

\[ \int \left (10 x-3 x^2+e^{2 e^{9 x^2}} \left (2 x+36 e^{9 x^2} x^3\right )\right ) \, dx=\int { -3 \, x^{2} + 2 \, {\left (18 \, x^{3} e^{\left (9 \, x^{2}\right )} + x\right )} e^{\left (2 \, e^{\left (9 \, x^{2}\right )}\right )} + 10 \, x \,d x } \]

[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)

Mupad [B] (verification not implemented)

Time = 12.94 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \left (10 x-3 x^2+e^{2 e^{9 x^2}} \left (2 x+36 e^{9 x^2} x^3\right )\right ) \, dx=x^2\,\left ({\mathrm {e}}^{2\,{\mathrm {e}}^{9\,x^2}}-x+5\right ) \]

[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)