3.151 \(\int a^x \, dx\)

Optimal. Leaf size=8 \[ \frac {a^x}{\log (a)} \]

[Out]

a^x/ln(a)

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, 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} \[ \frac {a^x}{\log (a)} \]

Antiderivative was successfully verified.

[In]

Int[a^x,x]

[Out]

a^x/Log[a]

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 {align*} \int a^x \, dx &=\frac {a^x}{\log (a)}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \[ \frac {a^x}{\log (a)} \]

Antiderivative was successfully verified.

[In]

Integrate[a^x,x]

[Out]

a^x/Log[a]

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fricas [A]  time = 0.42, size = 8, normalized size = 1.00 \[ \frac {a^{x}}{\log \relax (a)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a^x,x, algorithm="fricas")

[Out]

a^x/log(a)

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giac [A]  time = 1.15, size = 8, normalized size = 1.00 \[ \frac {a^{x}}{\log \relax (a)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a^x,x, algorithm="giac")

[Out]

a^x/log(a)

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maple [A]  time = 0.00, size = 9, normalized size = 1.12 \[ \frac {a^{x}}{\ln \relax (a )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a^x,x)

[Out]

a^x/ln(a)

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maxima [A]  time = 0.42, size = 8, normalized size = 1.00 \[ \frac {a^{x}}{\log \relax (a)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a^x,x, algorithm="maxima")

[Out]

a^x/log(a)

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mupad [B]  time = 0.16, size = 8, normalized size = 1.00 \[ \frac {a^x}{\ln \relax (a)} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(a^x,x)

[Out]

a^x/log(a)

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sympy [A]  time = 0.09, size = 8, normalized size = 1.00 \[ \begin {cases} \frac {a^{x}}{\log {\relax (a )}} & \text {for}\: \log {\relax (a )} \neq 0 \\x & \text {otherwise} \end {cases} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(a**x,x)

[Out]

Piecewise((a**x/log(a), Ne(log(a), 0)), (x, True))

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