MATEMATYKA193

376 Tablica całek nieoznaczonych

\/ax² + bx + c ^a_ ^2a

II jVk-x²dx-yxVk-x² + -ikarcsin-j*+C.

12. JVk + x²dx-=-ix\/k + x² + ikln|x+Vk + x²|+C

13. f V»x² t bx + cdx - ^Vax²1 bx te -y- f-T-~""

^{J 4i}> ®*² Vax²+bx+c

14 f <L_ = ' h<__a-

^J xvb±ax² Vb+vb±ax²

10.

,5j

Inj ——jl...... ł+C. a>0. b>0.

/b ±

1 ____Vb

xVax² - b

-priUtMIl-7=

Vb |x| va

+ C, a > O, b > 0

16. Jlnxdx = xlnx-x + C.

17. J_n = J(lnx)ⁿdx = x(lnx)ⁿ-nJ_n_,, n = l,2,... .

18. J„=/xV¹‘dx=ix"e“-|j_n.₁.

19 JP(x)c^,vdN = e*^x||P(x)-iP'(x>+...+(-l)ⁿ-L.p<ⁿ⁾(x)lfC. P(x) - wielomian stopnia n,

20. fc^axsinbxdx = -r-^—=-e*^x(asinbx-bcosbx) + C, a²+b²*0.

^J a²+b²

21. fc^,*cosbxdx*-T-~rC^flX(a(X)sbx + bsinbx)-fC, a²+b²*0.

^J a² + b²

22. Jxsin&xdx =» -^xcosax+-ysinax + C.

23. Jxⁿsinaxdx = -“Xⁿ cosax + ^Jx^n_lcosaxdx.

24. fxcosaxdx =-xsinax-ł--4-cosax + C.

J a a*

25. f xⁿ cosaxdx = -x" sin ax - - f x" ¹ sinaxdx.

J a a J

* = -IgT^⁺C. a*_±b

27. Jcosaxcosbxdx = * igfbj" *^C. **±b-

28 J sin ax cos bxdx = - ^co^ -^ + C ■ a * ±b

²⁹ fŁ-'^ f'^+C30J^^=ln|t8<f ⁺ f>l^+C-

31 J ₌f_dx_ ₌__!__ęo§K_ ₊ ILzlj , _n = 2 3 ...

' ⁿ J sin"x n-l_sin" ‘x n-l^J-²’

32. j_n= f—^ I -i|ax_₊n^2_J n = 2,3.....

j cosⁿx n -1 cos *x n-1

33. J. = fsin"xdx =-—sin" ¹ xcosx + -^^;:-^J_n ■>, n = 2,3,... .

" J n n ⁿ •

34. J„ = fcosⁿxdx = -cos" 'xsinx + ~^J_{B 2}, n = 2.3,...

" J n n

35. J„ =

c=^rftgⁿ'x-J_{n 2}, n = 2,3.....

76. J_n = Jctgⁿxdx = --jj4*jctgⁿ 'x — J_n_2♦ n = 2,3,... .