Need guidance please. I have an integral (sqrt(x^2+81)/2 dx. I know the 2 on the bottom is a constant but not sure how to start this prob,

Question

Need guidance please. I have an integral (sqrt(x^2+81)/2 dx.  I know the 2 on the bottom is a constant but not sure how to start this prob,

campbell_st · Answer

$$1/2\int\limits (x^2 +81)^{1/2} dx$$

anonymous · Answer

then do I use the power rule for this?

anonymous · Answer

Is this what it should look like?   $$1/2\int\limits (x^2 +81 )^ (3/2)   dx x( 2x)$$

anonymous · Answer

oops meant 3/2 in front not 1/2

campbell_st · Answer

I think you will need a substitution

anonymous · Answer

yes that is what I am suppose to do but didn't only see u being (x^2+81) and du being 2x not sure what v would be for this question.

campbell_st · Answer

have you done hyperbolic functions...?
 
as its $$1/2 \int\limits \sqrt{x^2 + 81} dx = \sinh(x/9)$$

anonymous · Answer

nope not yet.  3rd term calculus is what I am in.  Integration by parts is what we learned most recent.

anonymous · Answer

Does anyone know how to do this by integration by parts?