Help with some AP Calc. problems, please help me?

I will be truly grateful for any help.

1) S (sinx - 3cotxsinx) dx =

A. cosx +3cscx + C

B. cosx + 3sinx + C

C. -cosx -3sinx+C

D. -cosx +3cscx+C

E. none of the above

im thinking none of the above since the answer i got, had -cosx but did not have -3sinx or 3cscx

2. S (4x-8)/(X^2-4X+7)^6 dx =

A. (-4)/(x^2-4x+7)^5 + C

B. (-4)/(5)(x^2-4x+7)^5 + C

C. -2/(x^2-4x+7)^5 + C

D. -2/(5)(x^2-4x+7)^5 + C

E. none of these

I have done this problem two times and still can't get an answer even remotely close to any of the 4 answers... so im guessing it is none of these?

3) Solve the differential equation dy/dx = 3x^2 + sinx+2, if y=2 when x=0.

A. y=x^3-cosx+2x+3

B. y=x^3-cosx+2x+2

C. y=x^3+cosx+2x+1

D. y=x^3-cosx+2x+C

E. y=X^3+cosx+2x

I think it is D but not sure. I am just guessing since it should definitely be an equation with a -cosx and then I just guessed it was D out of A,B, and D.

4) S (sinx-3cotxsinx)dx=

A. cosx+3cscx + C

B. cosx + 3sinx + C

C. -cosx -3sinx + C

D. -cosx + 3cscx + C

E. none of above

I am guessing none of the above cuz the answer I found did not have 3cscx, 3sinx or -3sinx. but I am really prone to making mistakes and do not trust my answer.