\(\int e^x (6+6 x) \, dx\) [10201]

Optimal result

Integrand size = 9, antiderivative size = 15 \[ \int e^x (6+6 x) \, dx=-2-e^{e^8}+6 e^x x \]

[Out]

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

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2207, 2225} \[ \int e^x (6+6 x) \, dx=6 e^x (x+1)-6 e^x \]

[In]

Int[E^x*(6 + 6*x),x]

[Out]

-6*E^x + 6*E^x*(1 + x)

Rule 2207

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[(c + d*x)^m*
((b*F^(g*(e + f*x)))^n/(f*g*n*Log[F])), x] - Dist[d*(m/(f*g*n*Log[F])), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !TrueQ[$UseGamma]

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps \begin{align*} \text {integral}& = 6 e^x (1+x)-6 \int e^x \, dx \\ & = -6 e^x+6 e^x (1+x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.40 \[ \int e^x (6+6 x) \, dx=6 e^x x \]

[In]

Integrate[E^x*(6 + 6*x),x]

[Out]

6*E^x*x

Maple [A] (verified)

Time = 0.11 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.40

method	result	size
gosper	\(6 \,{\mathrm e}^{x} x\)	\(6\)
default	\(6 \,{\mathrm e}^{x} x\)	\(6\)
norman	\(6 \,{\mathrm e}^{x} x\)	\(6\)
risch	\(6 \,{\mathrm e}^{x} x\)	\(6\)
parallelrisch	\(6 \,{\mathrm e}^{x} x\)	\(6\)
parts	\(6 \,{\mathrm e}^{x} x\)	\(6\)
meijerg	\(6 \,{\mathrm e}^{x}-3 \left (2-2 x \right ) {\mathrm e}^{x}\)	\(15\)

[In]

int((6+6*x)*exp(x),x,method=_RETURNVERBOSE)

[Out]

6*exp(x)*x

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.33 \[ \int e^x (6+6 x) \, dx=6 \, x e^{x} \]

[In]

integrate((6+6*x)*exp(x),x, algorithm="fricas")

[Out]

6*x*e^x

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.33 \[ \int e^x (6+6 x) \, dx=6 x e^{x} \]

[In]

integrate((6+6*x)*exp(x),x)

[Out]

6*x*exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int e^x (6+6 x) \, dx=6 \, {\left (x - 1\right )} e^{x} + 6 \, e^{x} \]

[In]

integrate((6+6*x)*exp(x),x, algorithm="maxima")

[Out]

6*(x - 1)*e^x + 6*e^x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.33 \[ \int e^x (6+6 x) \, dx=6 \, x e^{x} \]

[In]

integrate((6+6*x)*exp(x),x, algorithm="giac")

[Out]

6*x*e^x

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.33 \[ \int e^x (6+6 x) \, dx=6\,x\,{\mathrm {e}}^x \]

[In]

int(exp(x)*(6*x + 6),x)

[Out]

6*x*exp(x)