Use the basic integration rules to find or evaluate the

Question

Use the basic integration rules to find or evaluate the integral.

1. ₁∫^{e ln?(2x)⁄x} dx
2. ∫^2x⁄((x-3)) dx

Use Integration by parts to find the indefinite integral.

3. ∫ x²  sin?(2x) dx
4. ∫x√(x-1) dx

Find the trigonometric integral.

5. ∫(sin?(πx⁄2))² dx
6. ∫cos?(πx-1))³    dx

Use trigonometric substitution to find or evaluate the integral.

7. ∫-12)⁄((x² √(4-x² ))) dx
8. ∫√(25-9x²) dx

Use partial fractions to find the indefinite integral.

9. ∫((x²+2x))⁄((x³-x²+x-1)) dx
10. ∫x²⁄((3(x-1)²)) dx