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Calculus  II                                              Test #3                                   April 15, 2005

Name____________________         R.  Hammack                               Score ______
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(1)   dx =   cos()2x dx = sin() + C

(2)   x (x)  dx = x tan(x)- tan(x)  dx = x tan(x)-ln| sec(x) | + C

(3)
sec(x)  dx = ln| sec(x) + tan(x) | + C

(4)   (x)dx =
x (x) - x dx =
x (x) + (-2x ) dx =
x (x) + + C =
x (x) + + C

(Using interation by parts with the following substitutions:)

(5) ∫   dx = -2∫ dx = -2∫   du =

+ C = + C =+ C

(6)   (x) (x) dx = (x) (x)cos(x) dx =

(x) (1-(x))cos(x) dx = (1-)du =-du =
-+C=-+ C

(7) ∫   dx = ∫   dx =

∫  du =() + C = () + C

(8)
dx =       dx = = (1) =

(9)   dx = +  dx =

dx + dx +   dx =
=ln(+2) + (x) -+ C

A =1
B =1
C = 2
D = 0

(10)      dx = sec(θ)tan(θ) dx =

dx =sec(θ) dx = ln| sec(θ) + tan(θ) | + C
=ln| x+tan((x)) |+C=ln| x +| + C

(11)   dx =

dx ===

(-+) = 0 + =

(12)
dx =
(Note: The integral is improper)

=3 dx = = = (6-6) = 6

(13)
= =

(14)
x == = 0