Inverse Trigonometric Functions: Integration 4.7 Inverse Trigonometric Functions: Integration and Completing the Square

Ex. Ex. Let u = 3x du = 3 dx

Ex. Integrate by substitution. Let u = ex du = ex dx

Ex. Rewriting the integrand as the sum of two quotients. Let u = 4 – x2 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. 1-29 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 Now complete the square in the denominator. Let u = x – 2 du = dx

Find the area of the region bounded by the graph of f(x) = , the x-axis, and and 2 1 1 2

Factor out a neg. inside the rad.

Adding and Subtracting Common Denominators The derivative of x2 + 2x + 2 is 2x + 2, so to get it, add and subtract 7 over x2 + 2x + 2. Now, put the first two term together. Now, integrate both terms. u’/u & arctan