\(\int 144 e^{-10+2 x+6 x^4} x (2+2 x+24 x^4) \, dx\) [6543]

Optimal result

Integrand size = 25, antiderivative size = 18 \[ \int 144 e^{-10+2 x+6 x^4} x \left (2+2 x+24 x^4\right ) \, dx=e^{-2+2 \left (-4+x+3 x^4+\log (12 x)\right )} \]

[Out]

exp(2*ln(12*x)+6*x^4+2*x-10)

Rubi [A] (verified)

Time = 0.03 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.72, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {12, 2326} \[ \int 144 e^{-10+2 x+6 x^4} x \left (2+2 x+24 x^4\right ) \, dx=\frac {144 e^{6 x^4+2 x-10} x \left (12 x^4+x\right )}{12 x^3+1} \]

[In]

Int[144*E^(-10 + 2*x + 6*x^4)*x*(2 + 2*x + 24*x^4),x]

[Out]

(144*E^(-10 + 2*x + 6*x^4)*x*(x + 12*x^4))/(1 + 12*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]]

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}& = 144 \int e^{-10+2 x+6 x^4} x \left (2+2 x+24 x^4\right ) \, dx \\ & = \frac {144 e^{-10+2 x+6 x^4} x \left (x+12 x^4\right )}{1+12 x^3} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.39 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int 144 e^{-10+2 x+6 x^4} x \left (2+2 x+24 x^4\right ) \, dx=144 e^{2 \left (-5+x+3 x^4\right )} x^2 \]

[In]

Integrate[144*E^(-10 + 2*x + 6*x^4)*x*(2 + 2*x + 24*x^4),x]

[Out]

144*E^(2*(-5 + x + 3*x^4))*x^2

Maple [A] (verified)

Time = 0.09 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94

method	result	size
risch	\(144 x^{2} {\mathrm e}^{6 x^{4}+2 x -10}\)	\(17\)
gosper	\({\mathrm e}^{2 \ln \left (12 x \right )+6 x^{4}+2 x -10}\)	\(18\)
default	\({\mathrm e}^{2 \ln \left (12 x \right )+6 x^{4}+2 x -10}\)	\(18\)
norman	\({\mathrm e}^{2 \ln \left (12 x \right )+6 x^{4}+2 x -10}\)	\(18\)
parallelrisch	\({\mathrm e}^{2 \ln \left (12 x \right )+6 x^{4}+2 x -10}\)	\(18\)

[In]

int((24*x^4+2*x+2)*exp(2*ln(12*x)+6*x^4+2*x-10)/x,x,method=_RETURNVERBOSE)

[Out]

144*x^2*exp(6*x^4+2*x-10)

Fricas [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int 144 e^{-10+2 x+6 x^4} x \left (2+2 x+24 x^4\right ) \, dx=e^{\left (6 \, x^{4} + 2 \, x + 2 \, \log \left (12 \, x\right ) - 10\right )} \]

[In]

integrate((24*x^4+2*x+2)*exp(2*log(12*x)+6*x^4+2*x-10)/x,x, algorithm="fricas")

[Out]

e^(6*x^4 + 2*x + 2*log(12*x) - 10)

Sympy [A] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int 144 e^{-10+2 x+6 x^4} x \left (2+2 x+24 x^4\right ) \, dx=144 x^{2} e^{6 x^{4} + 2 x - 10} \]

[In]

integrate((24*x**4+2*x+2)*exp(2*ln(12*x)+6*x**4+2*x-10)/x,x)

[Out]

144*x**2*exp(6*x**4 + 2*x - 10)

Maxima [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89 \[ \int 144 e^{-10+2 x+6 x^4} x \left (2+2 x+24 x^4\right ) \, dx=144 \, x^{2} e^{\left (6 \, x^{4} + 2 \, x - 10\right )} \]

[In]

integrate((24*x^4+2*x+2)*exp(2*log(12*x)+6*x^4+2*x-10)/x,x, algorithm="maxima")

[Out]

144*x^2*e^(6*x^4 + 2*x - 10)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int 144 e^{-10+2 x+6 x^4} x \left (2+2 x+24 x^4\right ) \, dx=e^{\left (6 \, x^{4} + 2 \, x + 2 \, \log \left (12 \, x\right ) - 10\right )} \]

[In]

integrate((24*x^4+2*x+2)*exp(2*log(12*x)+6*x^4+2*x-10)/x,x, algorithm="giac")

[Out]

e^(6*x^4 + 2*x + 2*log(12*x) - 10)

Mupad [B] (verification not implemented)

Time = 11.67 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int 144 e^{-10+2 x+6 x^4} x \left (2+2 x+24 x^4\right ) \, dx=144\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-10}\,{\mathrm {e}}^{6\,x^4} \]

[In]

int((exp(2*x + 2*log(12*x) + 6*x^4 - 10)*(2*x + 24*x^4 + 2))/x,x)

[Out]

144*x^2*exp(2*x)*exp(-10)*exp(6*x^4)