Evaluate the following integrals
Let
Let x=a tan2y
⇒ dx=2a tan y sec2y dy.
Also, when x=0, y=0
and when x=a,
Hence
Using integration by parts, we get
Let tan y=t
⇒ sec2ydy=dt.
Also, when y=0, t=0
and when , t=1.
Also, y=tan-1t
Let
Hence
Substituting value of I’ in I, we get