Evaluate

to solve this integral we have to apply substitution method for which we are going to put x=a.tan²k

_{This means dx = 2.a.tank.sec}²k.dk,then I will be,

In this above integral let tank =t then sec²kdk=dt ,put in above equation-

Apply the formula of sqrt(x²+a²)=x/2.sqrt(a²+x²)+a²/2ln|x+sqrt(a²+x²)|

Now put the value of t in above integral t=tank,then finally integral will be-

Now put the value of k in terms of x that is tan²k=x/a in above integral –