1.

Evaluate the following integrals :\(\int\frac{cosec^2x}{1+cotx}\)dx

Answer»

Assume,

1 + cotx = t 

d(1 + cotx) = dt 

⇒cosec2x = dt 

Put t and dt in given equation we get,

⇒ ∫\(\frac{dt}{t}\)

= ln|t| + c

But,

t = 1 + cotx 

= ln|1 + cotx| + c.



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