\subsubsection {}
Vy�et�ete konvergenci n�sleduj�c�ch
integr�l�: 

a) $\int_0^{\frac\pi2} {{\,\roman{d}x}\over \sin^p x\cos^q x}$

b) $\int_0^{\frac\pi2}{{\,\roman{d}x}\over \sin^q x(1-\sin
x)^p}$

c) $\int_1^\infty{{\,\roman{d}x}\over x^p \ln^q x} $

d) $\int_2^\infty{{\,\roman{d}x}\over x^p \ln^q x}$ 

e) $\int_e^\infty {{\,\roman{d}x}\over x^p(\ln x)^q(\ln\ln
x)^r} $

f) $\int_{e+1}^\infty {{\,\roman{d}x}\over x^p(\ln x)^q(\ln\ln
x)^r} $

g) $\int_0^\infty \sin x^2 {\,\roman{d}x}$




\subsubsection {}
Zjist�te, pro kter� $\alpha,\beta,\gamma\in\Bbb R$ konverguje
integr�l 

$$\int\limits_0^1 x^\gamma\cos
x\ln{x^\alpha+2x^\beta+1\over
2x^\beta+1}{\,\roman{d}x} \quad .$$ 


\subsubsection {}

Zjist�te, pro kter�
$\alpha,\beta,\gamma,\delta\in\Bbb R$
konverguje
integr�l $$\int\limits_0^1 e^{\frac\gamma x}x^\beta\sin
x\arctg{x^\alpha+1\over
x^\delta+1}{\,\roman{d}x}\qquad .$$     


\subsubsection {}
Vy�et�ete konvergenci Newtonov�ch integr�l�

1. $\int_0^\infty{\sin^2x\over x^\alpha}{\,\roman{d}x}$ 

2. $\int_0^\infty x^\alpha\arctg^\beta x{\,\roman{d}x}$

3. $\int_\alpha^\beta {\arcsin^2(\sin x)\over \sin x}{\,\roman{d}x}$\quad

4. $\int_0^1 x^{\log x}{\,\roman{d}x}$
\quad
$\int_0^1 x^{-\log x}{\,\roman{d}x}$\quad

5. $\int_0^1{\sqrt{x}\over\sqrt{1-x^4}}{\,\roman{d}x}$\quad

6. $\int_0^1{x^2{\,\roman{d}x}\over\root 3\of{\left(1-x^2\right)^5}}$\quad

7. $\int_0^1{{\,\roman{d}x}\over e^{\sqrt x}-1}{\,\roman{d}x}$\quad

8. $\int_0^1{\sqrt x {\,\roman{d}x}\over e^{\sin x}-1}$
 
9. $\int_0^1{{\,\roman{d}x}\over e^x-\cos x}$\quad

10. $\int_0^{\frac\pi2}{\log\sin x\over\sqrt x}{\,\roman{d}x}$\quad

11. $\int_1^\infty x^k{x-\sin x\over x+\sin x}{\,\roman{d}x}$\quad

12. $\int_2^\infty{{\,\roman{d}x}\over x^k\log x}$

13. $\int_0^\infty {x^k\over 1+x^t}{\,\roman{d}x}$\quad

14. $\int_0^{\frac\pi2}{1-\cos x\over x^m}{\,\roman{d}x}$\quad

15. $\int_0^\pi{{\,\roman{d}x}\over\sin^kx}$

16. $\int_2^\infty{{\,\roman{d}x}\over x\log^k x}$

17. $\int_0^{\frac\pi2}x^\alpha\left(\frac\pi2-x\right)^\beta
\tg^\gamma x{\,\roman{d}x}$\quad

18. $\int_0^\infty x^\alpha\arcsin{x\over x^2+1}\sin\frac1x{\,\roman{d}x}$

19. $\int_0^\infty e^{\alpha x^2+\beta x}x^\gamma\sin
x{\,\roman{d}x}$\quad


\subsubsection {}
 Vy�et�ete konvergenci (absolutn�, neabsolutn�)
n�sleduj�c�ch integr�l� 

1. $\int_0^\infty {\sin x\sin 2x\over x^\alpha}{\,\roman{d}x}$\quad 

2. $\int_0^\infty x^\alpha\ln(1+x)\cos x{\,\roman{d}x}$\quad

3. $\int_0^\infty \operatorname{arctg}^\alpha x{\sin\pi x\over \vert\ln
x\vert^\beta}{\,\roman{d}x}$

4. $\int_0^\infty \sin(\operatorname{arccotg} x)\sin x{\,\roman{d}x}$ \quad 

5. $\int_0^\infty{\sin x\over x+\cos x}{\,\roman{d}x}$\quad 

6. $\int_0^\infty{\sin x\over
\sqrt x+\cos x}{\,\roman{d}x}$

 7. $\int_0^\infty 2x\cos\left(x^4\right){\,\roman{d}x}$
\quad 

8. $\int_0^\infty x^p\sin\left(x^q\right){\,\roman{d}x}$ \quad

9. $\int_0^1{\sin\frac1x\over x}\operatorname{arctg} x{\,\roman{d}x}$ \quad

10. $\int_0^\infty {\sin\left(x+\frac1x\right)\over x^u}{\,\roman{d}x}$

