$\smallint \,\,\frac{{\cos \,\,x - \,\,\sin \,\,x}}{{1 + 2\,\,\sin \,\,x\,\,\cos \,\,x}}\,\,dx$ is equal to

$ - \,\,\frac{1}{{\cos \,\,x\,\, - \,\,\sin \,\,x}}\,\, + \,\,c$

$\frac{{\cos \,\,x\,\, + \,\,\sin \,\,x}}{{\cos \,\,x\,\, - \,\,\sin \,\,x}}\,\, + \,\,c$

$\frac{x}{{\sin \,\,x\,\, + \,\,\cos \,\,x}}\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{\cos \,\,x - \,\,\sin \,\,x}}{{1 + 2\,\,\sin \,\,x\,\,\cos \,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: C

- \,\,\frac{1}{{\sin \,\,x\,\, + \,\,\cos \,\,x}}\,\, + \,\,c

Option C (

\ - \,\,\frac{1}{{\sin \,x\, + \,\,\cos \,x}}\, + \,c

) is correct because it is the result of a u-substitution where

u = \sin x + \cos x