Recognizing Integrals
Although the integrals in each group have similarities, they require different
approaches. For each integral decide which of the following is needed: 1)
substitution, 2) algebra or a trig identity, 3) the function can be integrated
as it stands, or 4) the function cannot be integrated by the techniques in
Math 124. Then evaluate each integral (except for the 4th type). Each
problem contain one problem from each of the 4 categories.
1. A.
dxx )1(
3
B.
dxxx
432
)1(
C.
dxx
1
3
D.
dxx
23
)1(
2. A.
dxe
x
2
B.
dx
e
e
x
x
3
C.
dxe
x
)3(
D.
dx
x
e
x
2
2
)(ln
3. A.
dxxx )1(
2
B.
dxx
2
1
C.
dx
x
2
1
1
D.
2
1x
dxx
4. A.
dx
4
cos
B.
dxx
2
cos1
C.
xx
dx
sincos
D.
dx
x
x
sin
cos
5. A.
dxxtan
B.
dxxx tansec
C.
dxxx costan
D.
dxx
1
)1(tan