Page 228 - Calculus Demystified

Methods of Integration
CHAPTER 7
2. Use partial fractions to evaluate each of the following indefinite integrals. 215

dx
(a)
(x + 2)(x − 5)

dx
(b)
2
(x + 1)(x + 1)

dx
(c)
2
3
x − 2x − 5x + 6

xdx
(d)
4
x − 1

dx
(e)
2
3
x − x − 8x + 12

x + 1
(f)
3
2
x − x + x − 1
3. Use the method of u-substitution to evaluate each of the following indefinite
integrals.

2
2
(a) (1 + sin x) 2 sin x cos xdx
√

sin x
(b) √ dx
x

cos(ln x) sin(ln x)
(c) dx
x

2
(d) e tan x sec xdx

sin x
(e) dx
2
1 + cos x
2
sec x
(f) dx
2
1 − tan x
4. Evaluate each of the following indefinite trigonometric integrals.

2
(a) sin x cos xdx

2
3
(b) sin x cos xdx

2
3
(c) tan x sec xdx