Final answer:
To integrate the function ∫(lnx)^ndx, you can use integration by parts. Substitute u = (lnx)^n and dv = dx, then apply the integration by parts formula to get the answer.
Step-by-step explanation:
To integrate the function ∫(lnx)^ndx, you can use integration by parts.
Let u = (lnx)^n and dv = dx. Then, du = n(lnx)^(n-1)/x dx and v = x.
Applying the integration by parts formula, you get ∫(lnx)^ndx = uv - ∫v du.
Substituting the values, you obtain ∫(lnx)^ndx = x(lnx)^n - n∫(lnx)^(n-1)/xdx.