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# Evaluate the integral. (use c for the constant of integration.) (ln(x))^{2} dx

**Solution:**

Given function is (ln(x))^{2} dx

Let Integral I =∫(ln(x))^{2} dx ---------->(1)

Let us use integration by parts.

∫u. dv = uv - ∫v. du

∫u. dv = (ln(x))^{2} dx

Let u = (ln(x))^{2} and dv = dx

⇒du = 2 . ln x .1/x dx and v = x

Thus (1) becomes

= (ln(x))^{2}. x - ∫x. 2 . ln x .1/x dx

= x (ln(x))^{2}- ∫2 . ln x . dx

= x (ln(x))^{2}- 2 . (xln x -x)

= x (ln(x))^{2}- 2x.ln x + 2x + C

Thus ∫(ln(x))^{2} dx = x (ln(x))^{2}- 2x.ln x + 2x + C

## Evaluate the integral. (use c for the constant of integration.) (ln(x))^{2} dx

**Summary:**

Evaluating the integral (using c for the constant of integration) (ln(x))2 dx, we get x (ln(x))^{2}- 2x.ln x + 2x + C

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