Evaluate the integrals in Exercises 9–28. It may be necessary to use a substitution first.
∫ [x / (x² + 4x + 3)] dx

4. What substitutions are made to evaluate integrals of sin(mx)sin(nx), sin(mx)cos(nx), and cos(mx)cos(nx)? Give an example of each case.

Evaluate the integrals in Exercises 29–32 (b) using a trigonometric substitution.

∫ [x / √(4 − x²)] dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ sinx·cos²x dx

135. Evaluate ∫₀^(π/2) (sin x) / (sin x + cos x) dx in two ways:

(a) By evaluating ∫ (sin x) / (sin x + cos x) dx, then using the Evaluation Theorem.

Finding volume: Find the volume of the solid generated by revolving the region bounded by the x-axis and the curve y = x sin(x), 0 ≤ x ≤ π, about

a. The y-axis.

(See Exercise 57 for a graph.)

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ t dt / √(9 − 4t²)