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  • I have a doubt, kindly clarify. - Integral Calculus - JEE Main-12

Integrate \int \cot ^{5}x dx

  • Option 1)

    \frac{\cot ^{4}x}{4}- \frac{\cot ^{2}x}{2}+ C

  • Option 2)

    \frac{\cot ^{4}x}{4}- \frac{\cot ^{2}x}{2}+ln \sin x+ C

  • Option 3)

    \frac{\cot ^{4}x}{4}- {\cot ^{2}x}+ln \sin x+ C

  • Option 4)

    none of these

 

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=3

\int tan^{2}x.tanxdx

use tan^{2}x=sec^{2}x-1 and seperate

 

 \int \cot ^{5} x dx = \int \cot ^{3 }x (\csc ^{2}x-1) dx

= \int \cot ^{3}x \csc^{2 } x dx - \int \cot x \csc^{2}x dx + \int \cot x dx

\frac{\cot^{4}x}{4}- \frac{\cot ^{2}x}{2}+ ln \sin x + C

 

 

 


Option 1)

\frac{\cot ^{4}x}{4}- \frac{\cot ^{2}x}{2}+ C

This is incorrect

Option 2)

\frac{\cot ^{4}x}{4}- \frac{\cot ^{2}x}{2}+ln \sin x+ C

This is correct

Option 3)

\frac{\cot ^{4}x}{4}- {\cot ^{2}x}+ln \sin x+ C

This is incorrect

Option 4)

none of these

This is incorrect

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Plabita

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