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Evaluate the integral \int (\tan x )^{11}(\sec x)^{2}dx

  • Option 1)

    \frac{(\tan x)^{11}}{11}+ C

  • Option 2)

    \frac{(\tan x)^{12}}{12}+ C

  • Option 3)

    \frac{(\tan x)^{10}}{10}+ C

  • Option 4)

    \frac{(\tan x)^{13}}{13}+ 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)^{11}(\sec ^{2})xdx

put \tan = z; \sec^{2}x dx = dz

\Rightarrow \int z^{11} dz = \frac{z^{12}}{12}+ C 

\rightarrow \frac{(\tan x)^{12}}{12}+ C

 

 

 

 


Option 1)

\frac{(\tan x)^{11}}{11}+ C

This is incorrect

Option 2)

\frac{(\tan x)^{12}}{12}+ C

This is correct

Option 3)

\frac{(\tan x)^{10}}{10}+ C

This is incorrect

Option 4)

\frac{(\tan x)^{13}}{13}+ C

This is incorrect

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Aadil

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