Write a value of ∫(1 + cotx)/(x + log sinx)dx.\(\int\frac{1+cot\,x}

1.	Write a value of ∫(1 + cotx)/(x + log sinx)dx.\(\int\frac{1+cot\,x}{x+log\,sin\,x}\) dx
Answer» 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

Write a value of ∫(1 + cotx)/(x + log sinx)dx.\(\int\frac{1+cot\,x}{x+log\,sin\,x}\) dx

Answer»

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