फलन `int(cosx)/(cos 3x)` का मान ज्ञात कीजिए।

Explanation

`int(cosx)/(cos 3x)dx=int(cosx)/(4cos^(3)x-3cosx)dx=int(1)/(4cos^(2)x-3)dx`
`=int(1)/(4cos^(2)x-3(cos^(2)x+sin^(2)x))dx`
`=int(1)/(cos^(2)x-3sin^(2)x)dx=int(1)/(cos^(2)x(1-3tan^(2)x))dx`
`=int(sec^(2)x)/(1-3tan^(2)x)dx=(1)/(sqrt3)int(dt)/(1-t^(2))`
( यहाँ `sqrt3 tanx =t rArr sec^(2)x dx=(1)/(sqrt3)dt`)
`=(1)/(sqrt3).(1)/(2.1)log((1+t)/(1-t))+c`
`=(1)/(2sqrt3)log((1+sqrt3 tanx)/(1-sqrt3 tanx))+c`
`=(1)/(2sqrt3)log((1+sqrt3tanx)/(1-sqrt3tanx))+c`