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If I= int (sin 2x)/((3+4cosx)^(3))dx, t...

If `I= int (sin 2x)/((3+4cosx)^(3))dx,` then `I` equals

A

`(3cosx+8)/((3+4cosx)^(2))+C`

B

`(3+8cosx)/(16(3+4cosx)^(2))+C`

C

`(3+cosx)/((3+4cosx)^(2))+C`

D

`(3-8 cosx)/(16(3+4cosx)^(2))+C`

Text Solution

Verified by Experts

The correct Answer is:
b
We have, `I=2int(cosxsinx)/((3+4cos)^(3))dx`
`rArrI=-(1)/(2)int(cosx)/((3+4cosx)^3)d(3+4cosx)`
`rArrI=-(1)/(2)int(t-3)/(4t^(3))dt " where " t=3+4cosx`
`rArrI=(1)/(8)((1)/(t)-(3)/(2t^(2)))+C`
`rArrI=(2t-3)/(16t^(2))+C=(8 cosx+3)/(16(3+4cosx)^(2))+C`
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
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