1.1. ANTI-DERIVATIVES 11
3. ln.sec.x// CC D
Z
tan.x/ dx
4.
1
10
x
2
C 1
5
C C D
Z
x .x
2
C 1/
4
dx
5. ln.sec.x/ Ctan.x// C C D
Z
sec.x/ dx
6. .x 1/ e
x
C C D
Z
xe
x
dx
7.
1
2
ln
x 3
x 1
C C D
Z
dx
x
2
4x C 3
8. .x
3
3x
2
C 6x 6/e
x
C C D
Z
x
3
e
x
dx
Problem 1.14 Verify that
Z
dx
ax C b
D
1
a
ln.ax C b/ C C
Problem 1.15 Verify that
Z
e
ax
D
1
a
e
ax
C C
Problem 1.16 Verify that
Z
cos.ax C b/ D
1
a
sin.ax C b/
Problem 1.17 Verify that
Z
sec
2
.ax C b/ D
1
a
tan.ax C b/
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