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The value of integral dxcos3xsin2x can be expressed as  

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a
a rational function of tan x
b
an irrational function tan x
c
a rational function of cos x
d
a rational function of sin x

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detailed solution

Correct option is B

write the given integral as I=12∫dxcos4⁡xtan⁡xput tan⁡x=t to obtain I=12∫1+t2tdt=12∫t−1/2+t3/2dt=122t+25t5/2+C=2tan⁡x+15(tan⁡x)5/2+C.Thus, I is an irrational function of tan x


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