Question

Write a value of ∫(1 + cotx)/(x + log sinx)dx.

\(\int\frac{1+cot\,x}{x+log\,sin\,x}\) dx

Answer 1

Let x + log sin x = t 

Differentiating it on both sides we get, 

(1+cot x) dx = dt - i 

Given that,

 ∫(1 + cotx)/(x + log sinx)dx

Substituting i in above equation we get, 

= \(\int\frac{dt}{t}\)

= log t + c 

= log(x + log sin x ) + c