$\smallint \,\,\frac{1}{{{{\sin }^2}\,\,x\,\,.\,\,{{\cos }^2}\,\,x}}\;\,\,dx$ is equal to

$\sin \,\,x\,\, - \,\,\cos \,\,x\,\, + \,\,c$

$\cos \,\,x\,\, + \,\,\sin \,\,x\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{1}{{{{\sin }^2}\,\,x\,\,.\,\,{{\cos }^2}\,\,x}}\;\,\,dx

is equal to

View answer and explanation

Correct option: D

\tan \,\,x\,\, - \,\,\cot \,\,x\,\, + \,\,c

Option D (

\tan \,x\, - \,\cot \,x\, + \,c

) is correct because the integral simplifies to the sum of the integrals of sec²x and csc²x, which are tan x and -cot x, respectively.