How can I fix up the singularity?

[ftarak]

Homework Statement

I = \int^{2}_{0} (1-e^{-x})/\sqrt{x}

I=\int^{2}_{0.1}x/sin^2(x)

Homework Equations

The Attempt at a Solution

I tried to integrate by part, but I approached to trivial solution. I know that the answer is involved with Error function, but I don't know how I could reach the answer. so does anybody have any idea? please help.

 

[ftarak]

I am not sure but I am thinking about power series solution for the first integral. How can I fix up the singularity?

 

[╔(σ_σ)╝]

u^2 = x

 

[Char. Limit]

For the second one, integration by parts is your friend. Just remember to rearrange sin^2(x) first.

 

[ftarak]

thank you guys, your hints were so helpful.