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  • How to solve this problem- - Integral Calculus - JEE Main-9

Find the integration \int ( \tan x)^{3}\sec ^{4} x dx

  • Option 1)

    \frac{\tan ^{4}x }{4} + C

  • Option 2)

    \frac{\tan ^{6}x }{6}+\frac{\tan ^{4}x }{4}+C

  • Option 3)

    \frac{\tan ^{5}x }{5}+ C

  • Option 4)

    \frac{\tan ^{5}x }{5}+\frac{\tan ^{6}x }{6}+C

 

Answers (1)

best_answer

As we have learned

Special type of indefinite integration -

Integrals of the form :

(tan^{m}x)(sec^{n}x)

- wherein

Use 

sec^{2}x-tan^{2}x=1

 

 \int (\tan x)^{3} \sec ^{2}x\cdot \sec^{2}xdx

= \int \tan ^{3}x \sec^{2}xdx+ \int \tan ^{5}x\sec^{2} xdx

\frac{tan^{4}x}{4}+ \frac{\tan^{6}x}{6}+ C

 

 

 


Option 1)

\frac{\tan ^{4}x }{4} + C

This is incorrect

Option 2)

\frac{\tan ^{6}x }{6}+\frac{\tan ^{4}x }{4}+C

This is correct

Option 3)

\frac{\tan ^{5}x }{5}+ C

This is incorrect

Option 4)

\frac{\tan ^{5}x }{5}+\frac{\tan ^{6}x }{6}+C

This is incorrect

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