3.90.5 \(\int e^x \, dx\)

Optimal. Leaf size=5 \[ -1+e^x \]

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Rubi [A]  time = 0.00, antiderivative size = 3, normalized size of antiderivative = 0.60, number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2194} \begin {gather*} e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^x,x]

[Out]

E^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} &=e^x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 3, normalized size = 0.60 \begin {gather*} e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^x,x]

[Out]

E^x

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fricas [A]  time = 0.57, size = 2, normalized size = 0.40 \begin {gather*} e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x),x, algorithm="fricas")

[Out]

e^x

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giac [A]  time = 0.15, size = 2, normalized size = 0.40 \begin {gather*} e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x),x, algorithm="giac")

[Out]

e^x

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maple [A]  time = 0.02, size = 3, normalized size = 0.60

method	result	size
gosper	\({\mathrm e}^{x}\)	\(3\)
lookup	\({\mathrm e}^{x}\)	\(3\)
derivativedivides	\({\mathrm e}^{x}\)	\(3\)
default	\({\mathrm e}^{x}\)	\(3\)
norman	\({\mathrm e}^{x}\)	\(3\)
risch	\({\mathrm e}^{x}\)	\(3\)
meijerg	\({\mathrm e}^{x}-1\)	\(5\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x),x,method=_RETURNVERBOSE)

[Out]

exp(x)

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maxima [A]  time = 0.37, size = 2, normalized size = 0.40 \begin {gather*} e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x),x, algorithm="maxima")

[Out]

e^x

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mupad [B]  time = 0.01, size = 2, normalized size = 0.40 \begin {gather*} {\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x),x)

[Out]

exp(x)

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sympy [A]  time = 0.05, size = 2, normalized size = 0.40 \begin {gather*} e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x),x)

[Out]

exp(x)

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