Deriving some inverse trig functions and some integrals

Hi all!

I am having some trouble with a few problems I've been working on.

Find the derivatives of the function

$\displaystyle y = x^3arctan(1-x) + arcsin(2x) $

Step was was recognizing the product rule for $\displaystyle x^3acrtan(1-x) $

so I have $\displaystyle 3x^2arctan(1-x) + x^3(-1/(\sqrt{1-(-1)^2)} + 2/(\sqrt{1-(2x)^2}) $

but I am not sure that it is right

Problem number two: Find the derivative of

$\displaystyle y = tan(arccos(x)) + arccsc(3x^2) $

this one threw me a monkey wrench right away since the argument to arccos is only x and not a function of x. even if it were more then just x i'm still scratching my head on how to start this one

Problem three:

Intergrate

$\displaystyle /int 4 / (8 + 9x^2 -6x) $

I figured to used the identity that $\displaystyle \int du / (a^2 + u^2) = (1 / a)arctan(u/a) + C $

So I then went to complete the square to give me what I wanted

I got $\displaystyle [(3x)^2 + 2(3x) + 1^2 ] -1 $

so then my denominator turned into 7 + (3x+1)^2 which I figured was wrong. A little confused on this one.

Same for this last problem

$\displaystyle \int 5/(\sqrt{4-x^2+2x}) $

any help would be appreciated!!!