Integrating Reciprocals of Square Roots of Quadratics
To evaluatewe complete the square for the quadratic expression to obtainthen make the substitution simplify and integrate.
Complete the square to obtain
The integrand becomes
is a standard integral:Neverthelesscan be integrated by multiplyingby the fraction
The numerator is the differential of the denominator sinceand
To complete the integral we can either substitute back the original substitution to obtain
Now evaluate the limits