Answer :

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 –



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