SUBJECT: INTEGRAL CALCULUS FOR ENGINEERS

TOPIC: Miscellaneous Substitution u = (ax + b)^m

NOTE: Follow the formula and I need full complete solution and correct. Thanks you so much. Please help me!!

ACTIVITY # 6 (I NEED FULL COMPLETE SOLUTION AND READABLE.

GENERAL FORMULA WITH EXAMPLE (GUIDE FOR ACTIVITY):

\fLesson 14 - Miscellaneous Substitution u = (ax + b)m V When the integrand contains an irrational expression of the form (ax + b)m, where m and n are prime positive integers, then we substitute u = (ax + b)m. The process of solution is shown below. Example 1: J (x + 1) dx / (2x - 1 ) 3/4 ( S in terms of x ) > Ju Let u = (2x - 1 ) 1/4 u2 = (2x - 1 ) 2/4 = (2x - 1 ) 1/2 UE = (2x - 1 ) 3/4 u4 = (2x - 1 ) 4/4 u4 = 2x - 1 X = (u4+ 1) / 2 dx = 2u3 du = [[ (u4 + 1) / 2 + 1] ( 2 43 du ) / u3 = [ [(u4+ 1) + 2] du = ] (u4+ 3) du = 45 /5 + 3u + C 11 F1 = (2x - 1 ) 5/4 / 5 + 3(2x - 1 ) 1/4 + C final ans