Question

integrate, dx/(x^(n+1)+x)​

Answer 1

Answer:

∫dx/x^n+1 +x

∫dx/x(x^n +1)

=∫x^-1(x^n +1)^-1 dx

let x^n +1=t

nx^n-1 dx =dt

x^n-1 =dt/n

=∫x^n-1(x^n +1)^-1 /x^n   dx

=∫dt/n(t^-1)/t-1

=1/n∫dt/t(t-1)

=1/n{ln t-1 - ln t }

=1/n{ln (t-1 ) / t }

=1/n{ln x^n /( (x^n )+1 )}

Step-by-step explanation: