3.2.25 \(\int 2015^x \, dx\) [125]

3.2.25.1 Optimal result

Integrand size = 3, antiderivative size = 8 \[ \int 2015^x \, dx=\frac {2015^x}{\log (2015)} \]

output

2015^x/ln(2015)
 

3.2.25.2 Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int 2015^x \, dx=\frac {2015^x}{\log (2015)} \]

input

Integrate[2015^x,x]
 

output

2015^x/Log[2015]
 

3.2.25.3 Rubi [A] (verified)

Time = 0.13 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2624}

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

\(\displaystyle \int 2015^x \, dx\)

\(\Big \downarrow \) 2624

\(\displaystyle \frac {2015^x}{\log (2015)}\)

input

Int[2015^x,x]
 

output

2015^x/Log[2015]
 

3.2.25.3.1 Defintions of rubi rules used

rule 2624

Int[((F_)^(v_))^(n_.), x_Symbol] :> Simp[(F^v)^n/(n*Log[F]*D[v, x]), x] /; 
FreeQ[{F, n}, x] && LinearQ[v, x]
 

3.2.25.4 Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.12

method	result	size
gosper	\(\frac {2015^{x}}{\ln \left (2015\right )}\)	\(9\)
derivativedivides	\(\frac {2015^{x}}{\ln \left (2015\right )}\)	\(9\)
default	\(\frac {2015^{x}}{\ln \left (2015\right )}\)	\(9\)
parallelrisch	\(\frac {2015^{x}}{\ln \left (2015\right )}\)	\(9\)
norman	\(\frac {{\mathrm e}^{x \ln \left (2015\right )}}{\ln \left (2015\right )}\)	\(11\)
meijerg	\(-\frac {1-{\mathrm e}^{x \ln \left (2015\right )}}{\ln \left (2015\right )}\)	\(16\)
risch	\(\frac {31^{x} 13^{x} 5^{x}}{\ln \left (5\right )+\ln \left (13\right )+\ln \left (31\right )}\)	\(20\)

input

int(2015^x,x,method=_RETURNVERBOSE)
 

output

2015^x/ln(2015)
 

3.2.25.5 Fricas [A] (verification not implemented)

Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int 2015^x \, dx=\frac {2015^{x}}{\log \left (2015\right )} \]

input

integrate(2015^x,x, algorithm="fricas")
 

output

2015^x/log(2015)
 

3.2.25.6 Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62 \[ \int 2015^x \, dx=\frac {2015^{x}}{\log {\left (2015 \right )}} \]

input

integrate(2015**x,x)
 

output

2015**x/log(2015)
 

3.2.25.7 Maxima [A] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int 2015^x \, dx=\frac {2015^{x}}{\log \left (2015\right )} \]

input

integrate(2015^x,x, algorithm="maxima")
 

output

2015^x/log(2015)
 

3.2.25.8 Giac [A] (verification not implemented)

Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int 2015^x \, dx=\frac {2015^{x}}{\log \left (2015\right )} \]

input

integrate(2015^x,x, algorithm="giac")
 

output

2015^x/log(2015)
 

3.2.25.9 Mupad [B] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int 2015^x \, dx=\frac {{2015}^x}{\ln \left (2015\right )} \]

input

int(2015^x,x)
 

output

2015^x/log(2015)