The value of integral ∫dxcos3⁡xsin⁡2x can be expressed as  

The value of integral dxcos3xsin2x can be expressed as  

  1. A

    a rational function of tan x

  2. B

    an irrational function tan x

  3. C

    a rational function of cos x

  4. D

    a rational function of sin x

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    Solution:

    write the given integral as 

    I=12dxcos4xtanx

    put tanx=t to obtain 

    I=121+t2tdt=12t1/2+t3/2dt=122t+25t5/2+C=2tanx+15(tanx)5/2+C.

    Thus, I is an irrational function of tan x

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