Question

integration of e to the power logx

Answer 1

e^logx= x

So integration of e^logx =x^2/2

Answer 2

GIVEN :

The integration of e to the power logx

TO FIND :

The value of integration of e to the power logx

SOLUTION :

The integration of e to the power logx can be written as $\int e^{logx}dx$

Solving the given integration

$\int e^{logx}dx$

Let $y=e^{logx}$

Taking log on both the sides of the above equation

$logy=log(e^{logx})$

$logy=log(x)$  ( ∵ $e^{logx}=x$ )

$logy=logx$

⇒ y=x

Now the given integral becomes

$\int e^{logx}dx=\int xdx$

$=\frac{x^2}{2}+c$

∴ $\int e^{logx}dx=\frac{x^2}{2}+c$ where c is a constant.