JEE Main · 2004 · 24 Apr 2004 · Offline · Indefinite Integrals

\int \frac{d x}{c o s x - s i n x}

is equal to

Answer: (D)

Solution

Factor the denominator as

cos x - sin x = 2 cos (x + \frac{π}{4})

, so the integral becomes

\frac{1}{2} \int sec (x + \frac{π}{4}) d x

. Using

\int sec u d u = lo g tan (\frac{u}{2} + \frac{π}{4})

with

u = x + \frac{π}{4}

, the argument becomes

\frac{x}{2} + \frac{π}{8} + \frac{π}{4} = \frac{x}{2} + \frac{3 π}{8}

, so the integral equals

\frac{1}{2} lo g tan (\frac{x}{2} + \frac{3 π}{8}) + C

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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