
12-36 Calculus – Differentiation and Integration
11.
1
1
2
+
+
x
x
12.
sin( ) cos( )4 4x x
13.
3
5 7
2
2
e
e
x
x
+
14.
cos
sin
x
x1
2
+
15.
sec ( )
2
3 5x -
16.
sin(ln ) cos(ln )x x
x
+
17.
tanh x
Find the integrals of each of the following functions using the method of integration by parts:
18. x xtan
2
19. x x
2
ln
20. x e
x2 3-
21.
xe
x
x
( )1
2
+
22.
e x
x3
5sin
23.
x xlog( )1+
24.
tan
-1
x
25. x x
3 1
cot
-
26.
( )sinx x x
2
6 2 3+ −
27.
e bx
ax
cos
28. e bx
ax
sin
29. x x
n
ln
30. x xsec
2
31.
(ln )x
2
32.
(ln )x
3
33.
ln x
x
2