Math 1592 Calculus II - Sample Test 1 Solutions
tan-1 x dx
1.
Integration by parts. If u = tan-1 x, v = x, dx , dv = dx, du = 1 + x2 then tan-1 x dx = x tan-1 x - and if u = 1 + x2 , then du = 2xdx so tan-1 x dx = x tan-1 x - du 1 dx, 2 u 1 = x tan
Math 1592 Calc. II
.
Test 1
Integrate the following
(1)
1
tan 1 x dx ,
dx x2
(2)
ln x x
2
1
dx ,
(3)
0
x e x dx ,
(4)
3
sin 1 x dx ,
dx x2
5
, (6)
(5)
0 1
ln x dx , 1
(10)
0
(7)
sec3 x dx , (8)
,
4 3
2 x e x dx ,
(9)
3
sin 2 x co