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∫(lnx)^ndx=x(lnx)^n−n∫(lnx)^n−1dx

User Halloei
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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.

User Hungerstar
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