Integrations w/ trig substitutions, please?

Question

1. S (dx)/(4+x^2)^2 

2. S (square root of x^2-9)/x dx 

3. S x^3/(square root of 2-x^2) dx 

4. S dx/x^2(square root of 4x^2-9) dx 

5. S dx/(1-x^2)^3/2

 S represents integration

Answer 1

Substitution method

1)

Now the integral becomes

From pythagorean identity 1 + tan²(t) = sec²(t)

Apply the formula

Now

.

Answer 2

2)

Now the integral becomes

From pythagorean identity sec²(t) - 1 = tan²(t)

.

Answer 3

5)

Now the integral becomes

From pythagorean identity 1 - sin²(t) = cos²(t).

Answer 4

(3).

The solution as shown below.

Answer 5

(4).

The solution as shown below.