Page 229 - Calculus Workbook For Dummies

213
Chapter 11: Integration Rules for Calculus Connoisseurs

4. The a thing.
625 x - 121 tani 2 tani
2
=
11 = 625 x - 121 11
5. Substitute.
# dx
2
625 x - 121
11 sec tan di
i
i
= # 25 = 1 # sec di
i
11 tani 25
1
6. Integrate: = ln sec +i tani + C .
25
7. Switch back to x (look at Steps 3 and 4):
2
1 25 x 625 x - 121
= ln + + C
25 11 11
1 2 1
= ln 25 + 625 x - 121 - ln11 + C
x
25 25
1 2
x
= ln 25 + 625 x - 121 + C
25
2
r # 4 x - 1 dx = 4 x - 1 - arctan 4 x - 1 + C
2
2
x
2 1 2
x -
2 ^
1. Rewrite as = # x h dx.
2. Draw your triangle. See the following figure.
2x
2
√4x − 1

θ

1
2 x
3. Solve sec =i for x; get dx.
1
1 1
i
i
x = seci dx = sec tan di
2 2
4. Do the a thing.
2
1
4 x - = tani
5. Substitute.
2
# 4 x - 1 dx
x
= # tani $ 1 sec tan d = # tan i di
i i
i
2
1 seci 2
2