Basic Integration Formulas

∫k dx

kx + C

∫xⁿ dx

(xⁿ + 1) / (n + 1) for n ≠ -1, + C

∫dx/x

ln |x| + C

∫e^x dx

e^x + C

∫a^x dx

(a^x)/ ln a + C (a > 0, a doesn’t equal 1)

∫sinx dx

⁻cosx + C

∫cosx dx

sinx + C

∫sec²x dx

tanx + C

∫csc²x dx

⁻cotx + C

∫secxtanx dx

secx + C

∫cscxcotx dx

⁻cscx + C

∫tanx dx

ln |secx| + C

∫cotx dx

ln |sinx| + C

∫secx dx

ln |secx + tanx| + C

∫cscx dx

⁻ln |cscx + cotx| + C

∫sinhx dx

coshx + C

∫coshx dx

sinhx + C

∫dx/√a²-x²

arcsin(x/a) + C

∫dx/a² + x²

1/a arctan(x/a) + C

∫dx/ x√x² - a²

1/a arcsec|x/a| + C

∫dx/ √a² + x²

sinh⁻¹(x/a) + C (a > 0)

∫dx/ √x² - a²

cosh⁻¹(x/a) + C (x > a > 0)