3.103.74 \(\int (1-2 e^{1+2 x}) \, dx\)

Optimal. Leaf size=12 \[ 86-e^{1+2 x}+x \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2194} \begin {gather*} x-e^{2 x+1} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 - 2*E^(1 + 2*x),x]

[Out]

-E^(1 + 2*x) + x

Rule 2194

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 {gather*} \begin {aligned} \text {integral} &=x-2 \int e^{1+2 x} \, dx\\ &=-e^{1+2 x}+x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} -e^{1+2 x}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 - 2*E^(1 + 2*x),x]

[Out]

-E^(1 + 2*x) + x

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fricas [A]  time = 0.74, size = 10, normalized size = 0.83 \begin {gather*} x - e^{\left (2 \, x + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x - e^(2*x + 1)

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giac [A]  time = 0.16, size = 10, normalized size = 0.83 \begin {gather*} x - e^{\left (2 \, x + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x - e^(2*x + 1)

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maple [A]  time = 0.01, size = 11, normalized size = 0.92

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x-exp(2*x+1)

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maxima [A]  time = 0.37, size = 10, normalized size = 0.83 \begin {gather*} x - e^{\left (2 \, x + 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x - e^(2*x + 1)

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mupad [B]  time = 0.07, size = 10, normalized size = 0.83 \begin {gather*} x-{\mathrm {e}}^{2\,x+1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1 - 2*exp(2*x + 1),x)

[Out]

x - exp(2*x + 1)

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sympy [A]  time = 0.12, size = 7, normalized size = 0.58 \begin {gather*} x - e^{2 x + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x - exp(2*x + 1)

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