\(\int (-e^{3+e^5+x}+x^3) \, dx\) [4149]

Optimal result

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

[Out]

1/4*x^4-exp(exp(5)+3+x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2225} \[ \int \left (-e^{3+e^5+x}+x^3\right ) \, dx=\frac {x^4}{4}-e^{x+e^5+3} \]

[In]

Int[-E^(3 + E^5 + x) + x^3,x]

[Out]

-E^(3 + E^5 + x) + x^4/4

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}& = \frac {x^4}{4}-\int e^{3+e^5+x} \, dx \\ & = -e^{3+e^5+x}+\frac {x^4}{4} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \left (-e^{3+e^5+x}+x^3\right ) \, dx=-e^{3+e^5+x}+\frac {x^4}{4} \]

[In]

Integrate[-E^(3 + E^5 + x) + x^3,x]

[Out]

-E^(3 + E^5 + x) + x^4/4

Maple [A] (verified)

Time = 0.82 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83

method	result	size
derivativedivides	\(\frac {x^{4}}{4}-{\mathrm e}^{{\mathrm e}^{5}+3+x}\)	\(15\)
default	\(\frac {x^{4}}{4}-{\mathrm e}^{{\mathrm e}^{5}+3+x}\)	\(15\)
norman	\(\frac {x^{4}}{4}-{\mathrm e}^{{\mathrm e}^{5}+3+x}\)	\(15\)
risch	\(\frac {x^{4}}{4}-{\mathrm e}^{{\mathrm e}^{5}+3+x}\)	\(15\)
parallelrisch	\(\frac {x^{4}}{4}-{\mathrm e}^{{\mathrm e}^{5}+3+x}\)	\(15\)
parts	\(\frac {x^{4}}{4}-{\mathrm e}^{{\mathrm e}^{5}+3+x}\)	\(15\)

[In]

int(-exp(exp(5)+3+x)+x^3,x,method=_RETURNVERBOSE)

[Out]

1/4*x^4-exp(exp(5)+3+x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \left (-e^{3+e^5+x}+x^3\right ) \, dx=\frac {1}{4} \, x^{4} - e^{\left (x + e^{5} + 3\right )} \]

[In]

integrate(-exp(exp(5)+3+x)+x^3,x, algorithm="fricas")

[Out]

1/4*x^4 - e^(x + e^5 + 3)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.67 \[ \int \left (-e^{3+e^5+x}+x^3\right ) \, dx=\frac {x^{4}}{4} - e^{x + 3 + e^{5}} \]

[In]

integrate(-exp(exp(5)+3+x)+x**3,x)

[Out]

x**4/4 - exp(x + 3 + exp(5))

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \left (-e^{3+e^5+x}+x^3\right ) \, dx=\frac {1}{4} \, x^{4} - e^{\left (x + e^{5} + 3\right )} \]

[In]

integrate(-exp(exp(5)+3+x)+x^3,x, algorithm="maxima")

[Out]

1/4*x^4 - e^(x + e^5 + 3)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int \left (-e^{3+e^5+x}+x^3\right ) \, dx=\frac {1}{4} \, x^{4} - e^{\left (x + e^{5} + 3\right )} \]

[In]

integrate(-exp(exp(5)+3+x)+x^3,x, algorithm="giac")

[Out]

1/4*x^4 - e^(x + e^5 + 3)

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \left (-e^{3+e^5+x}+x^3\right ) \, dx=\frac {x^4}{4}-{\mathrm {e}}^3\,{\mathrm {e}}^{{\mathrm {e}}^5}\,{\mathrm {e}}^x \]

[In]

int(x^3 - exp(x + exp(5) + 3),x)

[Out]

x^4/4 - exp(3)*exp(exp(5))*exp(x)