MATH integral HARD help?

Question

2. integrate 1 / ((16-x^2)^(3/2)) dx by letting x = 4sin(t)
(integrate fully)

3. integrate 1 / ((x^2)((sqrt(25 + x^2))) dx by letter x = 5tan(t)

4. integrate 1 / (sqrt(8 + 2x - x^2)) dx

5.integrate from x=4 to x=0 1 / (sqrt(324+x^2)) dx

6. integrate from x=5(sqrt(2))/2 to x=0 (sqrt(25-(x^2))) dx

7. integrate 1 / (x^2)(sqrt(144-x^2)) dx

8. integrate (sqrt(16x-x^2)) dx

9. integrate 44 / (sqrt(40 - 6x - x^2)) dx

Answer 1

2. integrate 1 / ((16-x^2)^(3/2)) dx by letting x = 4sin(t)
(integrate fully)

∫1/((16 - x²)^(3/2)) dx

Let
x = 4sin(t)
dx = 4cos(t) dt

∫1/((16 - x²)^(3/2)) dx
= ∫{1/((16 - 16sin²t)^(3/2))}{4cos(t) dt}
= ∫{[4cos(t)]/(64cos³t)}dt
= ∫{1/(16cos²t)}dt
= ∫{sec²t/16}dt
= tan(t)/16 + C

x = 4sin(t)
sin(t) = x/4
tan(t) = x/√(16 - x²)

= tan(t)/16 + C
= x/{16√(16 - x²)} + C

Answer 2

not that hard, in fact is really easy, DO YOUR OWN HOMEWORK