Question

Evaluate : $\int 2^{x}dx$

Answer 1

$I=\int 2^{x}dx$

Let $2^x=t$

On taking log both sides, we get,

$x\log 2=\log t$

$\log 2dx=\frac{1}{t}dt$

$dx=\frac{1}{t\log 2}dt$

Therefore,

$I=\int \frac{tdt}{t\log 2}=\frac{1}{\log 2}\int dt$

$I=\frac{t}{\log 2}+C=\frac{2^x}{\log 2}+C$