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int("sin"(5x)/(3))/("sin"(x)/(2))dx is e...

`int("sin"(5x)/(3))/("sin"(x)/(2))dx` is equal to (where, C is a constant of integration)

A

`2x+sinx+sin2x+c`

B

`x+2sinx+sin2x+c`

C

`2x+sinx+2sin2x+c`

D

`x+2sinx+2sin2x+c`

Text Solution

Verified by Experts

The correct Answer is:
B
`int(sin5x/2)/(sinx/2)dx`
`impliesint(2.sin.(5x)/2cos.x/2)/(2sin.x/2cos.x/2)impliesint(2.sin.(5x)/2cos.x/2)/(sinx)`
`impliesint(sin3x+sin2x)/(sinx)impliesint(3sinx-4sin^3x+2sinxcosx)/(sinx)`
`impliesint(3-2(1-cos2x)+2cosx)dx`
`int(2cos2x+2cosx+1)dx`
`=sin2x+2sinx+x+C`
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