Table 8.1 Basic Integration Formulas

∫kdx

kx＋C, k real

∫(xⁿ)dx

x^(n+1)∕(n+1) +C

∫dx/x

ln |x| + C

∫e^(x)dx

e^x + C

∫a^xdx

a^x/ln(a) + C (a>0, a!=1)

∫sin(x)dx

-cos(x) + C

∫cos(x)dx

sin(x) + C

∫sec²(x)dx

tan(x)+C

∫csc²(x)dx

-cot(x) + C

∫sec(x)tan(x)dx

sec(x) + C

∫csc(x)cot(x)dx

-csc(x) + C

∫tan(x)dx

ln|sec(x)| + C

∫cot(x)dx

ln|sin(x)| + C

∫sec(x)dx

ln|sec(x)+tan(x)| + C

∫csc(x)dx

-ln|csc(x)+cot(x)| + C

∫sinh(x)dx

cosh(x) + C

∫cosh(x)dx

sinh(x) + C

∫dx/√(a² - x²)

sin⁻¹(x/a) + C, a>0

∫dx/a²+x²

1/a tan⁻¹(x/a) + C

∫dx/x√(x²-a²)

1/a sec⁻¹|x/a| + C

∫dx√(x²+a²)

sinh⁻¹(x/a) + C (a > 0)

∫dx√(x²-a²)

cosh⁻¹(x/a) + C (x > a > 0)