\(\int e^{2+2 x+x^5} (2+5 x^4) \, dx\) [273]

Optimal result

Integrand size = 18, antiderivative size = 14 \[ \int e^{2+2 x+x^5} \left (2+5 x^4\right ) \, dx=e^{2-x+x \left (3+x^4\right )} \]

[Out]

exp((x^4+3)*x-x+2)

Rubi [A] (verified)

Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {6838} \[ \int e^{2+2 x+x^5} \left (2+5 x^4\right ) \, dx=e^{x^5+2 x+2} \]

[In]

Int[E^(2 + 2*x + x^5)*(2 + 5*x^4),x]

[Out]

E^(2 + 2*x + x^5)

Rule 6838

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[q*(F^v/Log[F]), x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps \begin{align*} \text {integral}& = e^{2+2 x+x^5} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int e^{2+2 x+x^5} \left (2+5 x^4\right ) \, dx=e^{2+2 x+x^5} \]

[In]

Integrate[E^(2 + 2*x + x^5)*(2 + 5*x^4),x]

[Out]

E^(2 + 2*x + x^5)

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71

method	result	size
gosper	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)
derivativedivides	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)
default	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)
norman	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)
risch	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)
parallelrisch	\({\mathrm e}^{x^{5}+2 x +2}\)	\(10\)

[In]

int((5*x^4+2)*exp(x^5+2*x+2),x,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int e^{2+2 x+x^5} \left (2+5 x^4\right ) \, dx=e^{\left (x^{5} + 2 \, x + 2\right )} \]

[In]

integrate((5*x^4+2)*exp(x^5+2*x+2),x, algorithm="fricas")

[Out]

e^(x^5 + 2*x + 2)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.57 \[ \int e^{2+2 x+x^5} \left (2+5 x^4\right ) \, dx=e^{x^{5} + 2 x + 2} \]

[In]

integrate((5*x**4+2)*exp(x**5+2*x+2),x)

[Out]

exp(x**5 + 2*x + 2)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int e^{2+2 x+x^5} \left (2+5 x^4\right ) \, dx=e^{\left (x^{5} + 2 \, x + 2\right )} \]

[In]

integrate((5*x^4+2)*exp(x^5+2*x+2),x, algorithm="maxima")

[Out]

e^(x^5 + 2*x + 2)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.64 \[ \int e^{2+2 x+x^5} \left (2+5 x^4\right ) \, dx=e^{\left (x^{5} + 2 \, x + 2\right )} \]

[In]

integrate((5*x^4+2)*exp(x^5+2*x+2),x, algorithm="giac")

[Out]

e^(x^5 + 2*x + 2)

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79 \[ \int e^{2+2 x+x^5} \left (2+5 x^4\right ) \, dx={\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{x^5}\,{\mathrm {e}}^2 \]

[In]

int(exp(2*x + x^5 + 2)*(5*x^4 + 2),x)

[Out]

exp(2*x)*exp(x^5)*exp(2)