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Calculus/integration question
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hi :) i wanna u tell me the integration of : ln of X to tje powre of 2 over X multiply by radical of 1 + (ln of X )to the power of 2. i'll be garteful if u answer me soon
The question, restated, is the integeral(ln^2(x)/(x*(1+ln^2(x))).
This is a problem that requires three u substitutions, so we will take u as u, w, and w.
1) Do a u substitution with u=ln(x). This will elimnate the x since the derivative of ln(x) is 1/x.
2) Next let tan(v)=u, so sec(v) dv = u du. This reduces to the integral of tan(v).
3) Note that tan(v)=sin(v)/cos(v), so let w=cos(v) and note that dw = -sin(v) dv.
Note that -ln(w)=ln(1/w). Back substitue back to x, and you're done. There may be something about limits and which areas of x that can be used along the way.
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