If  \int \tan ^{4}xdx= \lambda \tan^{3}x + \mu \tan x+ x+ c,\, \, then

  • Option 1)

    \lambda =\frac{1}{3}

  • Option 2)

    \mu = 1

  • Option 3)

    \lambda =-\frac{1}{3}

  • Option 4)

    None of these

 

Answers (1)

 

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 ^{4}xdx=\lambda \tan ^{3}x+\mu \tan x+x+C

\int \tan ^{2}x.\tan ^{2}xdx

\int \tan ^{2}x.(\sec^{2}x -1)dx

=>\int \tan ^{2}x.\sec ^{2}xdx-\int \tan ^{2}xdx

=>\frac{\tan^{3} x}{3}-\tan x+x+C

\therefore \lambda =\frac{1}{3}, \: \mu =-1


Option 1)

\lambda =\frac{1}{3}

Option is Correct

Option 2)

\mu = 1

Option is incorrect

Option 3)

\lambda =-\frac{1}{3}

Option is incorrect

Option 4)

None of these

Option is incorrect

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