RECOGNIZING INTEGRALS
Name___________________________
Although the integrals in each group below 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) nothing needed, or 4) can’t be done by the techniques in Calculus I. Then evaluate each integral
(except for the 4th type of course).
1. A.
B.
x
3
 1 dx
2
3
 x  x  1 dx
4
C.

D.
x
x3  1dx
3
 1 dx
2
2. A.
e
 x2
dx
3. A.

x 1  x 2  dx
1  x 2 dx
B.
ex
 3  e x dx
B.

C.
 e
C.

D.

D.

x
 3 dx
ln  e2 x 
x
2
dx
1
1  x2
xdx
1  x2
dx
 
 cos  4  dx
5. A.
B.

1  cos 2 xdx
B.
 cos
C.
 cos x
dx
sin x
C.
 tan x cos xdx
D.

D.
 tan x  1
4. A.
cos x
dx
sin x
 tan(3x) sec(3x)dx
dx
2
x
dx