By: Tao Steven Zheng (鄭濤)

【Problem】

This problem is a good exercise on integration by parts and integration by substitution.
Compute the integral

【Solution】

Step 1：Integration by Parts

Let and .

Then and .

By the integration by parts

we get

Step 2：Integration by Substitution

Now focus on the integral . Use the substitution method for this integral.

Let , then .

Therefore,

Consequently, the complete integral is