Basic Integration Formulas.

APPENDIX B

Basic Integration
Formulas












a dx = ax + C
x r dx =

x r+1
+C

r+1

[r = −1]

1
dx = ln |x| + C
x

x
dx
1
= tan−1 + C
a
a
a2 + x 2

dx
x
= sin−1 + C [a > 0]
√

2
2
a
a −x

dx
x
1
= sec−1 + C [a > 0]
√
2
2
a
a
x x −a

ex dx = ex + C











ax dx =

ax
+C
ln a

[a > 0]

xex dx = ex (x − 1) + C
ln x dx = x ln x − x + C
sin x dx = − cos x + C





















tan x dx = ln |sec x| + C
sec x dx = ln |sec x + tan x| + C
cot x dx = ln |sin x| + C
csc x dx = ln |csc x − cot 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
sin2 x dx =

sin 2x
x
−
+C
2
4

cos2 x dx =

x

sin 2x
+
+C
2
4

tan2 x dx = tan x − x + C

cos x dx = sin x + C

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