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.sec2k.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 –