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Intergrate \int \tan ^{3 }x dx

  • Option 1)

    3/4 ln \sec x + C

  • Option 2)

    3/4 ln \ sec x -1/12 ln sec + C

  • Option 3)

    \sec x +C

  • Option 4)

    ln \sec ^{3} x + C

 

Answers (1)

best_answer

As we have learned

Integration of trigonometric function of power m -

\int tan^{m}xdx , \int cot^{m}xdx

 

 

- wherein

for m=2

use tan^{2}x=sec^{2}x-1  , cot^{2}x=cosec^{2}x-1

 

\int \tan^{3}x dx

=\int \frac{3 \tan x dx}{4}- \int \frac{\tan 3x dx }{4} 

=3/4 ln \sec x- 1/12 ln \sec 3x + C

 

 

 

 

 


Option 1)

3/4 ln \sec x + C

This is incorrect

Option 2)

3/4 ln \ sec x -1/12 ln sec + C

This is correct

Option 3)

\sec x +C

This is incorrect

Option 4)

ln \sec ^{3} x + C

This is incorrect

Posted by

gaurav

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