Hello!

I am going over some work for my midterm and some questions came up, and i was wondering if someone could help!

1) The integral of 1/((x^2)(x^2+9)^(1/2)

Clearly this is trig substitution...

x=3tangent

dx=3sec^2

(X^2+9)^1/2 = 3sec

Integral then becomes (1/27)(1/cos)/((sin^3)/(cos^3))

Integral turns into (Cot^2)(csc^2)

(I do not have the theta sign because i cant find it on my keyboard. When assume it is there after the tangent, cot, etc).

What do I do from there?

2) Is (n+1)! / n! = (n+1)n! / n!

3) The volume of the region, rotated about y=1, bounded by y=x^2 y=1 using cylindrical shells.

=2pi x Integral of ( ? )(y-y^2)dy

4) Compute the sum of the series as n -> infinity, starting at one, of ln (n/n+1). I know it is convergent, since the limit of n -> infinity of an goes to zero.

It is going to zero...

How do i find the sum?

Thank you all for your help! If I was unclear in the way I asked a question please let me know. This will help a lot.