Indefinite Integral problem

[cosmic]

Hi guys,

Using integration by substitution does the indefinite integral of sinx/(3+2 cosx)^2= 1/(6+4cosx) + c

I'd appreciate if someone could tell me whether I've calculated the correct answer or point me in the right direction if it's wrong.

Thanks in advance.

 

[JohnZ]

I think it is correct. you can always check your result by taking a derivative on right side.

 

[HallsofIvy]

Yes, that is correct. In future, it would be better to show how you got a result so that if it is NOT correct, we can make suggestions to improve.

I presume you first made the substitution u= cos(x) and then the substitution v= 3+ 2u.
(Or, if you are really good, the single substitution u= 3+ 2 cos(x))!)

 

[cosmic]

I think it is correct. you can always check your result by taking a derivative on right side.

Thanks John.

I forgot I could check it that way.

Yes, that is correct. In future, it would be better to show how you got a result so that if it is NOT correct, we can make suggestions to improve.

I presume you first made the substitution u= cos(x) and then the substitution v= 3+ 2u.
(Or, if you are really good, the single substitution u= 3+ 2 cos(x))!)

Thanks for the response.

And no I let u=3+2 cosx thus du/dx=-2 sin(x) and did the substitution that way.