Výsledky

 19. $-\frac13 \cos 3x + c$. 		 20. $-\frac13 \ln \vert 3x-5\vert + c$. 


 21. $-\frac12 e^{3-2x} + c$. 		 22. $\frac14 (3x-2) \sqrt[3]{3x-2} + c$. 


 23. $-\frac{(4-7x)^{12}}{84} + c$. 		 24. $\frac15 \mbox{tg}\,5x + c$. 


 25. $\arcsin \frac{x}{3} + c$. 		 26. $\frac14 \mbox{arctg}\,\frac{x}{4} + c$. 

 27. $\sqrt{x^2 - 4} + c$. 		 28. $\ln \vert 1 + \sin x\vert + c$. 


 29. $-\frac25 \sqrt{\cos^5 x} + c$. 		 30. $\frac12 e^{x^2} + c$. 


 31. $\ln \vert\ln x\vert + c$. 		 32. $\frac29 \sqrt{(x^3+1)^3} + c$. 


 33. $\mbox{arctg}\,\frac{\sqrt{x}}{2} + c$. 		 34. $\frac12 \mbox{arctg}\,x^2 + c$. 


 35. $\ln \vert e^{-x} - 1\vert + c$. 		 36. $\frac23 \sqrt{\mbox{arctg}\,^3 e^x} + c$. 


 37. $\arccos \frac{1}{x} + c$. 		 38. $\frac23 \sqrt{(x+1)^3} - 2 \sqrt{x+1}$.

Vo výsledkoch nasledujúcich cvičení je ešte pred výsledkom uvedená substitúcia, ktorou je možné integrál riešiť.

 39. $t = 4x - 11,\ I = \frac16 \sqrt{(4x-11)^3} + c$. 


 40. $t = 5 - 3x,\ I = -2 \ln \vert 5 - 3x\vert + c$. 


 41. $t = 4 + x^2,\ I = 2 \ln \vert 4 + x^2\vert + c$. 


 42. $t = 2x + 3,\ I = \frac{1}{(2x+3)^7} + c$. 


 43. $t = x^2 + 7,\ I = (x^2+7)^5 + c$. 


 44. $t = 3 - x^2,\ I = -\sqrt{3 - x^2} + c$. 


 45. $t = 1 + x^6,\ I = \frac13 \mbox{arctg}\,x^3 + c$. 


 46. $t = 4 - x^2,\ I = -\frac{5}{12} \sqrt[5]{(4-x^2)^6} + c$. 


 47. $t = \sin x,\ I = \frac17 \sin^7 x + c$. 


 48. $t = 2 + \cos x,\ I = -2 \sqrt{2 + \cos x} + c$. 


 49. $t = x+1,\ I = \mbox{arctg}\,(x+1) + c$. 


 50. $t = 2x - 1,\ I = \frac12 \arcsin(2x-1) + c$. 


 51. $t = \frac{1}{x},\ I = -e^{\frac{1}{x}} + c$. 


 52. $t = e^{x^2+4x-5},\ I = \frac12 e^{x^2+4x-5} + c$. 


 53. $t = \ln x,\ I = \frac15 \ln^5 x + c$. 


 54. $t = \sin(\ln x),\ I = \sin(\ln x) + c$. 


 55. $t = e^{\cos^2 x},\ I = -e^{\cos^2 x} + c$. 


 56. $t = \sin \sqrt{x},\ I = 2 \ln \vert\sin \sqrt{x}\vert + c$. 


 57. $t = \mbox{tg}\,x,\ I = \frac35 \sqrt[3]{\mbox{tg}\,^5 x} + c$. 


 58. $t = \mbox{cotg}\,x,\ I = -2 \sqrt{\mbox{cotg}\,x - 1} + c$. 


 59. $t = 2^x,\ I = \frac{\arcsin 2^x}{\ln 2} + c$. 


 60. $t = 4 + e^x,\ I = e^x - 4\ln \vert 4 + e^x\vert + c$. 


 61. $t = \mbox{arctg}\,x,\ I = \ln (\mbox{arctg}\,x) + c$. 


 62. $t = \ln x,\ I = 3 \arcsin (\ln x) + c$.