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int(sin2x)/(sin5xsin3x)dx is equal to...

`int(sin2x)/(sin5xsin3x)dx` is equal to

A

`log sin3x-log sin5x+c`

B

`(1)/(3)log sin3x+(1)/(5)log sin5x+c`

C

`(1)/(3)log sin3x-(1)/(5)log sin5x+c`

D

`3log sin3x-5log sin5x+c`

Text Solution

Verified by Experts

The correct Answer is:
C
`int(sin2x)/(sin5xsin3x)dx=int(sin(5x-3x))/(sin5xsin3x)`
`=int(sin5xcos3x-cos5xsin3x)/(sin5xsin3x)dx`
`=(1)/(3)logsin3x-(1)/(5)logsin5x+C`
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