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
answer is B.
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Detailed Solution
write the given integral as I=12∫dxcos4xtanxput tanx=t to obtain I=12∫1+t2tdt=12∫t−1/2+t3/2dt=122t+25t5/2+C=2tanx+15(tanx)5/2+C.Thus, I is an irrational function of tan x