integrate, dx/(x^(n+1)+x)
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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:
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