Integral Sheet
Preamble: This sheet contains all the integrals you will need to know for exam 1, on Feb 10. Anything on this sheet is fair game. Remember your arbitrary constants for indefinite integrals. You may not bring this sheet into exams. You must memorize it. Sums and products: cf (x)dx = c f (x)dx c a constant g(x)dx f (x)g (x)dx
f (x)±g(x)dx =
f (x)dx±
f (x)g(x)dx = f (x)g(x)− Elementary functions: xn dx = xn+1 +C n+1
if k = −1
cos xdx = sin x+C sin xdx = − cos x+C ex dx = ex +C 1 dx = ln |x|+C x sec2 xdx = tan x+C csc2 xdx = − cot x+C sec x tan xdx = sec x+C √ 1 dx = arcsin a2 − x2 x +C a x +C a
1 1 dx = arctan a2 + x2 a