Mohammad Motamed
MATH 316, Spring 2017
This integral table is to be used throughout the course. You are free to use it when doing
homework, in class, on exam, etc. The following table will be constantly updated as we face
new integrals. So, please check it regularly for updates. In any case, it is recommended that
you know how to integrate and derive the formulas yourself.
1
a
R
ea x dx =
R
x ea x dx =
R
eax cos(bx) dx =
a cos(b x)+b sin(b x)
a2 +b2
ea x
R
eax sin(bx) dx =
a sin(b x)−b cos(b x)
a2 +b2
ea x
ea x
a x−1
a2
ea x
x ex cos x dx = 12 ex x cos x + (x − 1) sin x
R
x ex sin x dx = 12 ex x sin x − (x − 1) cos x
R 1
dx = a1 ln |a x + b|
a x+b
R 1
dx = a1 tan−1 xa
a2 +x2
R x
dx = 12 ln |a2 + x2 |
a2 +x2
R x2
dx = x − a tan−1 xa
a2 +x2
R