MATH 136, section 1 – Calculus 2 Integration By Substitution Practice February 7, 2014

Each of the following integrals can be done by the method of u-substitution: 1. Determine the appropriate function u,

2. Compute du,

3. Change the integral to an equivalent form in the new variable u. If it is a definite integral, you can convert the limits of integration as well.

4. Integrate, then

5. Resubstitute u to express the answer in terms of the original variable (indefinite integral cases), or evaluate (definite integral cases).

• ∫ x\sqrt{x^{2} + 16} dx

• ∫ cos θe^{1+sin θ} dθ

• ∫_{π/4}^{π/2} cos^{3}(4θ) sin(4θ) dθ

• ∫ \frac{1}{\sqrt{1 − 4x^{2}}} dx

• ∫_{0}^{1/4} \frac{x}{\sqrt{1 − 4x^{2}}} dx

• ∫ \frac{1}{x ln(x)} dx

• ∫ \frac{cos(\sqrt{y})}{\sqrt{y}} dy.