INTEGRAL CHEAT SHEET V2 (1220-5 CALCULUS II, FALL 2006)
AREND BAYER, JWB 330
You will be allowed to use this page for reference in the midterm and the final exam. All integrals listed here can be used without justification. (1) xr dx = (2) ex dx = ex + C (10) (3) For a > 0, a = 1: ax ax dx = +C ln a (4) sin xdx = − cos x + C (12) (5) √ cos xdx = sin x + C (13) (6) (sec x)2 dx = 1 dx = (cos x)2 tan x + C 1 dx = (sin x)2 − cot x + C √ (14) √ (15) x2 1 1 x dx = tan−1 + C 2 +a a a x2 1 x dx = cosh−1 + C 2 a −a x 1 dx = sinh−1 + C a x2 + a2 a2 1 x dx = sin−1 + C 2 a −x sinh xdx = cosh x + C (11) cosh xdx = sinh x + C +C ln|x| + C
xr+1 r+1
(8) if r = −1 if r = −1 (9) cot xdx = ln|sin x| + C tan xdx = − ln|cos x| + C
(7) (csc x)2 dx =