MATH215 Lecture 6: note6

• School: University of Alberta
• Department: Mathematics
• Course: MATH215
• Professor: Alexander Litvak

Document Summary

Z ex dx = ex + c, xm+1 m + 1. Z sin x dx = cos x + c, dx = ln|x| + c. Z cos x dx = sin x + c. Z sec2 x dx = tan x + c, dx. 1 + x2 = arctan x + c, Z csc2 x dx = cot x + c. 1 x2: change of variables interval i and f is continuous on i, then. If u = g(x) is a di erentiable function whose range is an. Z f (g(x))g (x) dx = z f (u) du. Using the substitution u = sin x, du = cos x dx, we obtain. Z sin3 x cos x dx = z u3 du = u4. We make the substitution u = 1 + x3; du = 3x2 dx. Then x2 dx = (1/3) du, so we obtain.