ACTIVITY: Evaluate the following: x2 dx 1 . x2+4 (x+4)dx 2. J (x+2)vx+5 3. [x5 v4+ xdx dx 4 . x2(4+x3)2/3LESSON 13: TECHNIQUES OF INTEGRATION - ALGEBRAIC SUBSTITUTIONS VIII. Algebraic Substitutions Objectives: 1. Convert integrand into something that can be solved using previously discussed theorems 2. Make the integration of complicated functions easier 3. Transform the integrand into a different algebraic expression that is easier to integrate. T58] When the integrand contains fractional powers of x or (a + bx), Use the substitution z= Vx - z" = x or z = va+bx - z" = a+ bx Where: n = least common denominator (LCD) of the fractional powers T59] When the integrand contains the expression xm (a + bx) Where m, n, p, q are integers (n, q > 0), AND IF m+1 = integer, use the substitution z = Va + bx" or z* = a + bx n T60] When the integrand contains the expression xm (a + bx" ) a Where m, n, p, q are integers (n, q > 0), AND IF m+1 -+ 2 = integer, use the substitution x"z! = a + bx n