Wydział WILiŚ, Budownictwo i Transport, sem.1
dr Jolanta Dymkowska
Całka niewłaściwa
Oblicz:
" " "

1 x
1. e-20x dx 2. dx 3. dx
1+x2 x2+4
0 0 1
" "
0
1 1
4. ex dx 5. dx 6. dx
x-1 x2+x3
-" 2 1
" " "

1 ln x
7. dx 8. ln x dx 9. dx
x+x3 x
1 1 1
" " "

arctg x
ln x
10. dx 11. dx 12. e-x sin 2x dx
x2 1+x2
1 0 0
" " "

arctg x
1 2x+1
13. dx 14. dx 15. dx
x2 x2+2x+10 x2+2x+2
1 -" -"
" -1
0
1 cos x
" "1
16. dx 17. dx 18. dx
3
1+sin2 x x 3-x
(x-2)2
-" 0 -"
" " "

1 x2 1
19. dx 20. dx 21. dx
x4+x2 x3+8 5x2-4x+1
1 -" -"
1 1 e
1
"
22. dx 23. ln x dx 24. x ln x dx
x
0 0 0
1 1 2
1 1 1
" "
25. dx 26. dx 27. dx
1-x2 1-x x ln x
0 0 1
Ą Ą
1 2 2
0
x
e x
28. dx 29. tg x dx 30. dx
x3 cos2 x
-1 0 0
9 1 2
1 1
" "1 dx
31. dx 32. 33. dx
3
x2+4x-5
x-1
|x|
1 -2 0
0 2 4
1 1 1
" "
34. dx 35. dx 36. dx
2x+1 x ln2 x
x(4-x)
1
1 1
-
2
"
3 1 1
1 1 - ln x
"
37. dx 38. arctg x dx 39. dx
x2 x
-x2+4x-3
1 0 0
8

x
40. dx
8-x
0