\[\begin{array}{l}
 T1. \to \int {dx}  = x + C \\ 
 T2. \to \int {{x^n}dx}  = \frac{{{x^{n + 1}}}}{{n + 1}} + C \\ 
 T3. \to \int {\frac{{dx}}{x}}  = \ln x + C \\ 
 T4. \to \int {{e^x}} dx = {e^x} + C \\ 
 T5. \to \int {{a^x}} dx = \frac{{{a^x}}}{{\ln a}} + C \\ 
 T6. \to \int {\sin xdx}  =  - \cos x + C \\ 
 T7. \to \int {\cos xdx}  = \sin x + C \\ 
 T8. \to \int {\frac{{dx}}{{{{\cos }^2}x}}}  = {\mathop{\rm tg}\nolimits} x + C \\ 
 T9. \to \int {\frac{{dx}}{{{{\sin }^2}x}}}  =  - {\mathop{\rm ctg}\nolimits}  + C \\ 
 T10. \to \int {\frac{{dx}}{{\sqrt {1 - {x^2}} }}}  = \arcsin x + C =  - \arccos  + C \\ 
 T11. \to \int {\frac{{dx}}{{1 + {x^2}}}}  = {\mathop{\rm arctg}\nolimits} x + C =  - {\mathop{\rm arcctg}\nolimits} x + C \\ 
 T12. \to \int {\sinh xdx}  = \cosh x + C \\ 
 T13. \to \int {\cosh xdx}  = \sinh x + C \\ 
 T14. \to \int {\frac{{dx}}{{{{\cosh }^2}x}}}  = {\mathop{\rm tgh}\nolimits} x + C \\ 
 T15. \to \int {\frac{{dx}}{{{{\sinh }^2}x}}}  =  - {\mathop{\rm ctgh}\nolimits} x + C \\ 
 T16. \to \int {\frac{{dx}}{{1 - {x^2}}}}  = \frac{1}{2}\ln \left| {\frac{{1 + x}}{{1 - x}}} \right| + C = {\mathop{\rm arctgh}\nolimits} x + C \\ 
 T17. \to \int {\frac{{dx}}{{{x^2} - 1}}}  = \frac{1}{2}\ln \left| {\frac{{x - 1}}{{x + 1}}} \right| + C =  - {\mathop{\rm arcctgh}\nolimits} x + C \\ 
 T18. \to \int {\frac{{dx}}{{\sqrt {{x^2} + 1} }}}  = \ln \left( {x + \sqrt {{x^2} + 1} } \right) + C = {\mathop{\rm arcsinh}\nolimits} x + C \\ 
 T19. \to \int {\frac{{dx}}{{\sqrt {{x^2} - 1} }}}  = \ln \left( {x + \sqrt {{x^2} - 1} } \right) + C = {\mathop{\rm arccosh}\nolimits} x + C \\ 
 \end{array}\]