1. ∫ [u(x)] u (x)dx = r + 1 + C, r = −1 2. ∫ u∨(x) u(x) dx = ln|u(x)| + C

Table of Integrals
1.
Z
2.
Z
3.
Z
eu(x) u0 (x) dx = eu(x) + C
4.
Z
sin [u(x)] u0 (x) dx = − cos u(x) + C
5.
Z
cos [u(x)] u0 (x) dx = sin u(x) + C
6.
Z
tan [u(x)] u0 (x) dx = ln | sec u(x)| + C
7.
Z
cot [u(x)] u0 (x) dx = ln | sin u(x)| + C
8.
Z
sec [u(x)] u0 (x) dx = ln | sec u(x) + tan u(x)| + C
9.
Z
csc [u(x)] u0 (x) dx = ln | csc u(x) − cot u(x)| + C
ur+1 (x)
+ C, r 6= −1
[u(x)] u (x) dx =
r+1
r 0
u0 (x)
dx = ln |u(x)| + C
u(x)
10.
Z
sec2 [u(x)] u0 (x) dx = tan u(x) + C
11.
Z
csc2 [u(x)] u0 (x) dx = − cot u(x) + C
1
12.
Z
sec [u(x)] tan [u(x)] u0 (x) dx = sec u(x) + C
13.
Z
csc [u(x)] cot [u(x)] u0 (x) dx = − csc u(x) + C
14.
Z
15.
Z
1
u(x)
u0 (x)
dx = tan−1
+C
2
2
a + u (x)
a
a
16.
Z
u(x)
1
u0 (x)
p
+C
dx = sec−1
2
2
a
a
u(x) u (x) − a
17.
Z
sinh [u(x)] u0 (x) dx = cosh u(x) + C
18.
Z
cosh [u(x)] u0 (x) dx = sinh u(x) + C
19.
Z
sin−1 [u(x)] u0 (x) dx = u(x) sin−1 u(x) +
20.
Z
tan−1 [u(x)] u0 (x) dx = u(x) tan−1 u(x) −
21.
Z
u0 (x)
−1
p
dx = sin
a2 − u2 (x)
−1
u(x)
+C
a
0
−1
sec [u(x)] u (x) dx = u(x) sec
2
p
1 − u2 (x) + C
1
ln [1 + u2 (x)] + C
2
p
u(x) − ln |u(x) + u2 (x) − 1 + C