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Question
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Options
`log (sin^(-4/7) x) + c`
`(4)/(7)tan^(4/7) x + c`
`-(7)/(4)tan^(-4/7) x + c`
`log (cos^(3/7) x) + c`
Solution
`-(7)/(4)tan^(-4/7) x + c`
[ Hint : `int cos^(-3/7)x sin^(-11/7)x*dx`
= `int (sin^(-11/7)x)/(cos^(-11/7)x*cos^2x)*dx`
= `int tan^(-11/7)x sec^2x*dx`
Put tan x = t].
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