indefinite integrals, calculus homework help

  

attached below
lab3__1_.pdf

Unformatted Attachment Preview

Mth 252 Lab: The Substitution Rule (Change of Variables)
The purpose of this lab is to practice using The Substitution Rule. It will probably be
most helpful to you to work each of these by yourself and then discuss them in your
groups.
Evaluate the following indefinite integrals. Show the change of variables used for each
problem. Check your work by differentiation.
1.
∫ 2x ( x
2.
∫ 8x cos ( 4x
3.
∫ sin
4.
∫
3
2
)
2
)
+ 3 dx
x cos x dx
6x + 1
3x 2 + x
(
4
+ 1 dx
)
x +1
dx
13.
∫ (x
14.
∫ 3x − 1 dx
15.
∫ sin(5x)
16.
∫e
17.
∫ (6x − 1)
18.
∫ 16x
+ 8)5 x dx
3/2
5
−6 x
dx
dx
4
5.
∫
6.
∫ sec (5x) dx
2 x
dx
2
5
1
2
dx
4
+1
dx
⎛1
2⎞
⎜⎝ + 6x ⎟⎠ dx
x
7.
e2 x
∫ e2 x + 1 dx
19.
∫ ( ln x + 2x
8.
∫ cos
sin x
dx
4
x
20.
∫ (sinθ + 6 ) e
9.
∫x e
21.
∫ tan
10.
∫
22.
∫ sin ( tan z − π ) sec
2 x 3 +1
dx
4
1 − 9x
2
dx
1
dx
11. ∫
x(ln x + 3)5
12.
 
sec 2 x
∫ tan x + 5 dx
7
3
−5
−10
cos θ − 6θ
dθ
θ sec 2 θ dθ
6
( arctan x )4
23.
∫
24.
6x 2
∫ 2x 3 + 5 dx
Page  92  
)
1 + x2
dx
2
z dz
…
Purchase answer to see full
attachment