7.3 Integration Techniques
Question #3 (Medium): Evaluating the Integral Using Secant Substitution
If it contains the expression √ then let and using the identity ,
simplify the expression. Then after the integral is solved, work with a right angle triangle and replace
by substituting back in the original variable .
Evaluate the integral.
Since the denominator is in the form of √ , secant substitution is used. Let , then
. Then:∫ ∫ . Simplifying:
√ √ ( )
∫ ∫ √ . Based on the identity :
∫ ∫ ∫
Use integration by parts to solve. Let and , and , then
. Thus: [ ] [