For each of these integrals, choose the method that will work best on the integral.
You do no...
Mathematics, 25.04.2020 04:04 marine7643
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
Answers: 2
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