For each of these integrals, choose the method that will work best on the integral.
You do not have to compute the integrals.

(a)

4
x2 ? 25dx
integral. gif
integration by parts

substitution with u = x2

substitution with u = x2 ? 25

partial fractions

(b)

4
sqrt1a. gif x2 ? 25dx
integral. gif
integration by parts

substitution with u = x2 ? 25

partial fractionsinverse trig substitution

(c)

x2 sin(3x) dx
integral. gif
substitution with u = x2

inverse trig substitution partial fractionsintegration by parts

(d)

?/4 tan3(x) sec2(x) dx
integral. gif
0
substitution with u = tan(x)

partial fractions inverse trig substitutionintegration by parts

(e)

1
4x + 12
x2 + 6x + 10dx
integral. gif
0
integration by partspartial fractions

substitution with u = x2 + 6x + 10

substitution with u = 4x + 12

(f)

4 cos3(x) sin2(x) dx
integral. gif
1
integration by parts

change cos2x into 1 ? sin2x, then substitution with u = sin x

partial fractions

change sin2x into 1 ? cos2x, then substitution with u = cos x

(g)

25
5
x2 + 5x ? 14dx
integral. gif
16
partial fractionsintegration by parts inverse substitution with u =

sqrt1a. gif x
(i. e., x = u2)

substitution with u = x2 + 5x ? 14

(h)

2 x
sqrt1a. gif 5?x2) dx
integral. gif
0
integration by parts with u =

sqrt1a. gif 5?x2
and dv = x dxpartial fractions

substitution with u = 5 ? x2

inverse substitution with u =

sqrt1a. gif x
(i. e., x = u2)

(i)

1 sin(
sqrt1a. gif x) dx
integral. gif
0
partial fractionsinverse substitution with u =

sqrt1a. gif x
(i. e., x = u2) integration by parts with u = 1 and dv = sin(

sqrt1a. gif x
) dxinverse trig substitution

(j)

4
sin(ln x)
xdx
integral. gif
1
substitution with u = ln x

integration by parts with u = sin(ln x) and dv =

1
x
dx partial fractionsinverse trig substitution

(k)

2 ln(3x) dx
integral. gif
1
inverse trig substitution

integration by parts with u = ln(3x) and dv = dx

integration by parts with u = 1 and dv = ln(3x)dx

partial fractions

(l)

4
5
x ln xdx
integral. gif
2
substitution with u =

1
x
integration by parts with u =

5
x
and dv =

1
ln x
dx integration by parts with u =

1
ln x
and dv =

5
x
dx

substitution with u = ln x

(m)

4
3
(x2 + 2)3/2dx
integral. gif
1
substitution with u = x2 + 2

partial fractions integration by partsinverse trig substitution

(n)

5
abs1.gifx ? 3
abs1.gifdx
integral. gif
0
integration by partsinverse trig substitution split up the integral into

3
integral. gif
0
and

5
integral. gif
3
split up the integral into

2
integral. gif
0
and

5
integral. gif
2