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

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

[Out]

a^x/Log[a]

_______________________________________________________________________________________

Rubi [A]  time = 0.00475623, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{a^x}{\log (a)} \]

Antiderivative was successfully verified.

[In]  Int[a^x,x]

[Out]

a^x/Log[a]

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 0.564855, size = 5, normalized size = 0.62 \[ \frac{a^{x}}{\log{\left (a \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(a**x,x)

[Out]

a**x/log(a)

_______________________________________________________________________________________

Mathematica [A]  time = 0.000856275, size = 8, normalized size = 1. \[ \frac{a^x}{\log (a)} \]

Antiderivative was successfully verified.

[In]  Integrate[a^x,x]

[Out]

a^x/Log[a]

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 9, normalized size = 1.1 \[{\frac{{a}^{x}}{\ln \left ( a \right ) }} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(a^x,x)

[Out]

a^x/ln(a)

_______________________________________________________________________________________

Maxima [A]  time = 1.40368, size = 11, normalized size = 1.38 \[ \frac{a^{x}}{\log \left (a\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a^x,x, algorithm="maxima")

[Out]

a^x/log(a)

_______________________________________________________________________________________

Fricas [A]  time = 0.213548, size = 11, normalized size = 1.38 \[ \frac{a^{x}}{\log \left (a\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a^x,x, algorithm="fricas")

[Out]

a^x/log(a)

_______________________________________________________________________________________

Sympy [A]  time = 0.065949, size = 8, normalized size = 1. \[ \begin{cases} \frac{a^{x}}{\log{\left (a \right )}} & \text{for}\: \log{\left (a \right )} \neq 0 \\x & \text{otherwise} \end{cases} \]

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))

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.198347, size = 11, normalized size = 1.38 \[ \frac{a^{x}}{{\rm ln}\left (a\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a^x,x, algorithm="giac")

[Out]

a^x/ln(a)