Evaluate: \(\int\frac{cos^2x.cotx}{4 + 5cos^2x}dx\)

1.	Evaluate: \(\int\frac{cos^2x.cotx}{4 + 5cos^2x}dx\)
Answer» \(\int\frac{cos^2x.cotx}{4 + 5cos^2x}dx\) = \(\int\frac{\frac{-1}{10}dx}{t} = \frac{-1}{10}\)logt + c = log(4 + 5cosec²x) + c put 4 + 5 cosec²x = t – 10 cosec x – cosec x × cot x dx = dt cosec²x . cotxdx = \(\frac{-1}{10}\)dt

Answer»

\(\int\frac{cos^2x.cotx}{4 + 5cos^2x}dx\)

= \(\int\frac{\frac{-1}{10}dx}{t} = \frac{-1}{10}\)logt + c

= log(4 + 5cosec²x) + c

put 4 + 5 cosec²x = t

– 10 cosec x – cosec x × cot x dx = dt

cosec²x . cotxdx = \(\frac{-1}{10}\)dt

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