More U-Substitution: The “Double-U” Substitution with ArcTan(u). Chapter 5.5 February 13, 2007. Techniques of Integration so far…. Use Graph & Area ( ) Use Basic Integral Formulas Simplify if possible (multiply out, separate fractions…) Use U-Substitution….
February 13, 2007
Substitution Rule for Definite Integrals
Still have an extra “x” that can’t be related to the substitution.
U-substitution cannot be used for this integral
We have the formula:
Factor out the 9 in the expression 9 + t2:
Factor out the a2 in the expression a2 + t2:
We now have the formula:
It’s necessary to know both forms:
t2 - 2t +26 and 25 + (t-1)2
t2 - 2t +26 = (t2 - 2t + 1) + 25 = (t-1)2+ 25
Ans: The equation x2 + x + 3 has NO REAL ROOTS (Check b2 - 4ac)
If the equation has real roots, it can be factored and later we will use Partial Fractions to integrate.