Basic Integration Formulas

Math 222 Basic integrations to memorize

∫k dx

kx + C

∫xⁿ dx

(xⁿ⁺¹/n+1) + C

∫dx/x

ln|x| + C

∫e^x dx

e^x + C

∫a^x dx

(a^x)/(ln|a|) + C

∫sin(x)dx

-cosx + c

∫cos(x)dx

sinx + c

∫sec²(x)dx

=tanx+c

∫csc²(x)dx

−cot(x)+C

∫sec(x)tan(x)dx

= secx + C

∫csc(x)cot(x)dx

−cscx+C

∫tan(x)dx

ln|sec(x)| + C

∫cot(x)dx

ln I sinx I +c

∫sec(x)dx

ln I secx+tanx I +c

∫csc(x)dx

-ln|cscx + cotx|+c

∫sinh(x)dx

cosh(x)+C

∫cosh(x)dx

sinh(x)+C

∫dx/√a²-x²

sin⁻¹(x/a)+C

∫dx/a²+x²

(1/a)tan⁻¹(x/a) + C

∫dx/(x√x²-a²)

(1/a)sec⁻¹|x/a|+c

∫dx/√a²+x²

sinh⁻¹(x/a)+c (a>0)

∫dx/√x²-a²

cosh⁻¹(x/a)+c (x>a>0)