Basic Integration Formulas
Basic Integral Properties (C is the constant of integration, k and a are
constants, and n is any real number):
R
dx = x + C
R
kf (x)dx = k
R
[f (x) + g(x)]dx =
R
f (x)dx +
R
R
R
f (x)dx
n+1
xn dx = xn+1 + C
g(x)dx
Integrals With Logarithmic and Exponential Functions:
R 1
x dx = ln |x| + C
ex dx = ex + C
R
R
x
ax dx = lna a + C
Integrals of Trigonometric Functions:
R
sin xdx = − cos x + C
R
R
tan xdx = − ln | cos x| + C
R
sec xdx = ln | sec x + tan x|+C
R
sec2 xdx = tan x + C
R
sec x tan xdx = sec x + C
R
cos xdx = sin x + C
R
cot xdx = ln | sin x| + C
R
csc xdx = − ln | csc x + cot x|+C
csc2 xdx = − cot x + C
R
csc x cot xdx = − csc x + C
Integrals Involving Inverse Trigonometric Functions:
R
√ dx
= arcsin x + C
1−x2
R
R
dx
= arctan x + C
1+x2
R
R
√dx
= arcsec x + C
|x| x2 −1
dx
− √1−x
= arccos x + C
2
dx
− 1+x
2 = arccot x + C
R
1
− |x|√dx
= arccsc x + C
x2 −1