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Find the integral \int \sec ^{2}x \csc ^{2}x dx

  • Option 1)

    \csc x+\sec x +C

  • Option 2)

    \cot x+ \tan x+ C

  • Option 3)

    \csc^{2} x+\sec^{2} x +C

  • Option 4)

    \sin x + \cos x+ C

 

Answers (1)

\int \sec ^{2}x \csc ^{2}xdx [\because \sec^{2}x \csc^{2}x= \sec^{2}x+\csc ^{2}x]

=\int (\sec^{2}x+\csc ^{2}x)dx

= \tan x + \cot x + C


Option 1)

\csc x+\sec x +C

This is incorrect

Option 2)

\cot x+ \tan x+ C

This is correct

Option 3)

\csc^{2} x+\sec^{2} x +C

This is incorrect

Option 4)

\sin x + \cos x+ C

This is incorrect

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