Find the partial fraction decomposition -

Question

Calculate the integral-

1. ∫(x²/√(9-x²)) dx

2. ∫x/(1-x²)^3/2 dx

3. ₀∫⁴x²√(16-x²) dx

4. ∫1/e^x√(e^2x + 4) dx

5. ∫x/√(4x-x²) dx

6. ∫(7/(x-2)(x+5)) dx

7. ∫(x+3/x²-3x+2)dx

8. ∫(2x-1/(x-2)²(x+1)²) dx

9. ∫x⁵/(x³-1) dx

Find the partial fraction decomposition

10. x/(x⁴-1)