Wydział WILiŚ, Budownictwo i Transport, sem.1
dr Jolanta Dymkowska
Całka nieoznaczona - ciąg dalszy
Zad.1 Oblicz:

dx 3 dx
1.1 1.2 dx 1.3
(1+3x)4 (4x-15)5 x2-2x+50

dx -x 4x+5
1.4 1.5 dx 1.6 dx
x2-6x+13 x2-6x+10 x2-6x+13

3x+4 dx 2 dx
1.7 dx 1.8 dx 1.9 dx
2x2+2x+1 8x2-x x2+2x

5x+3 dx 2x+21
1.10 dx 1.11 1.12 dx
x2-9 2x2-7x+3 2x2+9x-5

dx x x2
1.13 1.14 dx 1.15 dx
x2(x2+4) (x-2)(x2+2x+5) (x+3)(x2-2x+10)

dx x2-3 x
1.16 1.17 dx 1.18 dx
x(x-1)2 x(x+1)2 (x2-4)2

x3-4 dx 2x
1.19 dx 1.20 1.21 dx
x3+4x (x+1)2x3 x4+6x2+25

dx dx dx
1.22 1.23 1.24
x4-8x2+16 x3+2x2+x+2 9x3-6x2+4x

2x5-x x5+2 3x3
1.25 dx 1.26 dx 1.27 dx
(x+1)3 x4-1 x2+x-2

x+1 x2 x3-2x-1
1.28 dx 1.29 dx 1.30 dx
(x-3)2 (x+2)2(x+4)2 x2-1

x3+x2+1 2x5+6x3+1 x3-3x2+5x-9
1.31 dx 1.32 dx 1.33 dx
x3+x2 x4+x2 x2-3x


1 x dx dx
" " " " "
1.34 dx 1.35 1.36
4 3 4
x2 x+1 x+ x+ x
x-1+ x-1
" " "

x ( x+1)2 x+ 2x-3
1.37 dx 1.38 dx 1.39 dx
x+2 x x-1
" " "

4 3
x2+ 1+x x+2 2-3x
" " " "
1.40 dx 1.41 dx 1.42 dx
3 3 6
1+x x( x+4 x) 2-3x-8


x 9x+1
" "
1.43 dx 1.44 dx
3 4
2-x
3x+4+ 3x+4

dx dx dx
" " "
1.45 1.46 1.47
x2+2x+2 9x2-36 16x2+40x+50

4x-3 -6x-5 4x-1
" " "
1.48 dx 1.49 dx 1.50
2 2
x2+6x+5
"-x -3x-2 "x -10x+9
36x+1
"
1.51 dx 1.52 x2 - 6x + 5 dx 1.53 16x2 + 40x + 50 dx
9x2+6x+5

1.54 sin3 x dx 1.55 cos7 x dx 1.56 sin4 x cos5 x dx

cos3 x
1.57 sin2 x cos7 x dx 1.58 sin3 x cos2 x dx 1.59 dx
sin5 x

1 sin x 3+sin x
1.60 dx 1.61 dx 1.62 dx
cos3 x cos3 x 1+cos x

1 sin x 1-cos x
1.63 dx 1.64 dx 1.65 dx
sin x+7 cos x 3 sin x+2 cos x-2 4+5 sin x

1 1 1
1.66 dx 1.67 dx 1.68 dx
sin2 x+sin x 4+sin2 x 5-4 sin x+3 cos x

1 1 cos2 x
1.69 dx 1.70 dx 1.71 dx
sin2 x+4 cos2 x sin4 x+4 cos2 x 3 sin2 x cos2 x-4 sin2 x

cos3 x
1.72 dx
2 sin3 x-sin2 x+sin x
Zad.2 Oblicz:
"
3
dx dx
" "
2.1 2.2 4x3 - 7 x2 dx 2.3
x( x-6) 9x2+4

dx x dx
"
2.4 2.5 2.6 sin(2 - 3x) dx
16-9x4
9-25x2

cos(ln x)
dx ex
"
2.7 2.8 dx 2.9 dx
x(ln2 x+4) x
25-e2x

x
2.10 ln - 1 dx 2.11 ln2(4x - 3) dx 2.12 x cos(2x - 1) dx
2

ln(x+1)-ln x
x2 1
" "
2.13 dx 2.14 dx 2.15 dx
x(x+1)
ex x 1+ln x

"
sin3 x
"
2.16 cos3 x sin x dx 2.17 dx 2.18 sin2 x + sin x cos x dx
3
cos2 x

sin 2x
"
2.19 dx 2.20 sin2 x cos2 x dx 2.21 x2 sin2 x dx
sin2 x+2 sin x+2

arcsin x
2.22 dx 2.23 x arcctg x dx 2.24 arccos (x + 1) dx
x2
"

arctg x
dx
"
2.25 dx 2.26 x4 ln x dx 2.27
x x(ln2 x+1) ln x
" "
2.28 ln(x2 + 1) dx 2.29 arcsin x + 1 dx 2.30 9 - ex dx

ln(x2-x+1)
dx ln sin x
2.31 2.32 dx 2.33 dx
1+ex x2 sin2 x


arccos ex 2x2+1 x+1
2.34 dx 2.35 arctg x dx 2.36 arccos dx
ex x2+1 x+2
"

x "
tg x
"xe
2.37 dx 2.38 cos2 x dx 2.39 dx
sin 2x
1+ex

"

3
1- xarctg x
dx 1
"x
2.40 2.41 dx 2.42 dx
3
sin x cos x ln2(tg x) x 1+ x (x2+1)2