Analiza Matematyczna- I Rok Informatyki
Lista 8
Obliczyć następujące całki nieoznaczone:

(x2-1)3
(1) dx (2) (x2 + 4)5xdx
x

xdx xdx
(3) (4)
x2+1 (x2+3)6
" "
" " "
3 4
3 4
x x+ x x-2 x2+4 5x3
"
(5) dx (6) dx
3
x2 6 x
"

"xdx
(7) ax + bdx (8)
3
2x2-1

x-1 x2dx
" "
(9) dx (10)
3 5
x+1
x3+1
1

2
x
e
(11) dx (12) xe-x dx
x2

dx
(13) (14) x sin(2x2 + 1)dx
2 cos2 3x

cos xdx
"
(15) sin5 x cos xdx (16)
1+sin x

x2dx
(17) cos x � esin xdx (18)
cos2(x3+1)

(ln x)2
dx
(19) dx (20)
x ex+e-x

exdx
(21) (22) x ln(1 + x2)dx
2ex+1
"

2+ln|x|
(23) dx (24) 61-xdx
x

ln | arc tg x|dx
dx
"
(25) (26)
1+x2
x 1-ln2 |x|

2
x2dx
"
(27) xex (x2 + 1)dx (28)
1-x6

(29) xexdx (30) x4exdx

(31) x cos xdx (32) x3 sin xdx

(33) ex cos xdx (34) ln xdx

(35) (ln x)3dx (36) arc tg xdx

ln xdx
(37) arc sin xdx (38)
x2

xdx
(39) (40) arc cos2 xdx
sin2 x

(41) x3(ln x)2dx (42) xn ln xdx, n = -1.