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Question
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Solution
Let I = `int (1 + x)/(x.sin (x + log x)).dx`
= `int (1)/(sin(x + logx)).((1 + x)/x).dx`
= `int (1)/(sin(x + log x)).(1/x + 1).dx`
Put x + log x = t
∴ `(1 + 1/x).dx` = dt
∴ I = `int (1)/sint dt = int "cosec" t dt`
= log |cosec t – cot t| + c
= log |cosec(x + log x) – cot(x + logx)|+ c.
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