5.7 Inverse Trigonometric Functions: Integration and Completing the Square

Ex. Let u = 3x du = 3 dx

Ex. Integrate by substitution. Let u = e x du = e x dx

Ex. Rewriting the integrand as the sum of two quotients. Let u = 4 – x 2 du = -2x dx Final Answer

Ex. Integrating an improper rational function. Do long division and then rewrite the integrand as the sum of two quotients odd

Ex. Completing the Square Let u = x – 2 du = dx

Ex. Completing the square when the leading coefficient is not 1. First, factor out a 1/2 Let u = x – 2 du = dx Now complete the square in the denominator.

Find the area of the region bounded by the graph of f(x) =, the x-axis, and and

Factor out a neg. inside the rad odd, 53, 55, 63, 65

Adding and Subtracting Common Denominators The derivative of x 2 + 2x + 2 is 2x + 2, so to get it, add and subtract 7 over x 2 + 2x + 2. Now, put the first two term together. Now, integrate both terms. u’/u & arctan