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

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

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

4. Ex. Rewriting the integrand as the sum of two quotients.
Let u = 4 – x2
du = -2x dx
Final Answer

5. Ex. Integrating an improper rational function.
Do long division and then rewrite the
integrand as the sum of two quotients.
1-29 odd

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

7. 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

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

9. Factor out a neg. inside the rad.

10. 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