solve ∫(dx/(x(xn +1))

Dear harshit agarwal

∫(dx/(x(xⁿ +1))

multiply and devide by x^n-1

integral will become

∫(x^n-1dx/(xⁿ(xⁿ +1))

put xⁿ=t

     nx^n-1dx^=dt

now integral will become

1/n∫(dt/(t(t +1))

=(1/n)∫(dt/[(t +1/2)²-(1/2)²]

this can be easly solve

by using the formula for

∫(dt/[(t)²-(a)²]

 just put

logx = y

1/xdx=dy

∫dy/e^ny  +1

from here you put take e^ny in numerator and put e^-ny +1 = z

you will get answer