\(\int (1-2 e^{1+2 x}) \, dx\) [10274]

Optimal result

Integrand size = 11, antiderivative size = 12 \[ \int \left (1-2 e^{1+2 x}\right ) \, dx=86-e^{1+2 x}+x \]

[Out]

x+86-exp(1+2*x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2225} \[ \int \left (1-2 e^{1+2 x}\right ) \, dx=x-e^{2 x+1} \]

[In]

Int[1 - 2*E^(1 + 2*x),x]

[Out]

-E^(1 + 2*x) + x

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}& = x-2 \int e^{1+2 x} \, dx \\ & = -e^{1+2 x}+x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int \left (1-2 e^{1+2 x}\right ) \, dx=-e^{1+2 x}+x \]

[In]

Integrate[1 - 2*E^(1 + 2*x),x]

[Out]

-E^(1 + 2*x) + x

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92

method	result	size
default	\(x -{\mathrm e}^{1+2 x}\)	\(11\)
norman	\(x -{\mathrm e}^{1+2 x}\)	\(11\)
risch	\(x -{\mathrm e}^{1+2 x}\)	\(11\)
parallelrisch	\(x -{\mathrm e}^{1+2 x}\)	\(11\)
parts	\(x -{\mathrm e}^{1+2 x}\)	\(11\)
derivativedivides	\(-{\mathrm e}^{1+2 x}+\frac {\ln \left ({\mathrm e}^{1+2 x}\right )}{2}\)	\(19\)

[In]

int(-2*exp(1+2*x)+1,x,method=_RETURNVERBOSE)

[Out]

x-exp(1+2*x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (1-2 e^{1+2 x}\right ) \, dx=x - e^{\left (2 \, x + 1\right )} \]

[In]

integrate(-2*exp(1+2*x)+1,x, algorithm="fricas")

[Out]

x - e^(2*x + 1)

Sympy [A] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.58 \[ \int \left (1-2 e^{1+2 x}\right ) \, dx=x - e^{2 x + 1} \]

[In]

integrate(-2*exp(1+2*x)+1,x)

[Out]

x - exp(2*x + 1)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (1-2 e^{1+2 x}\right ) \, dx=x - e^{\left (2 \, x + 1\right )} \]

[In]

integrate(-2*exp(1+2*x)+1,x, algorithm="maxima")

[Out]

x - e^(2*x + 1)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (1-2 e^{1+2 x}\right ) \, dx=x - e^{\left (2 \, x + 1\right )} \]

[In]

integrate(-2*exp(1+2*x)+1,x, algorithm="giac")

[Out]

x - e^(2*x + 1)

Mupad [B] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (1-2 e^{1+2 x}\right ) \, dx=x-{\mathrm {e}}^{2\,x+1} \]

[In]

int(1 - 2*exp(2*x + 1),x)

[Out]

x - exp(2*x + 1)