1.ʃdx = x + C 2. ʃ xⁿdx = $\frac{1}{n + 1}$xⁿ⁺¹ 3. ʃ xdx = $\frac{1}{2}$x² +C 4. ʃ $\frac{\mathbf{1}}{\mathbf{x}}$dx = ln|x| + c 5. ʃ a^xdx = $\frac{a^{x}}{\text{lna}}$ + C 6. ʃe^x = e^x + C 7. ʃ sinxdx = -cosx + C 8. ʃ cosxdx = sinx + C 9. ʃ tgxdx = -ln|cosx| + C 10. ʃ ctgxdx = ln|sinx| + C 11. ʃ $\frac{\mathbf{\text{dx}}}{\mathbf{\cos}^{\mathbf{2}}\mathbf{x}}$ = tgx + C 12. ʃ $\frac{\mathbf{\text{dx}}}{\mathbf{\sin}^{\mathbf{2}}\mathbf{x}}$ = - ctg + C 13. ʃ$\frac{\mathbf{\text{dx}}}{\mathbf{x}^{\mathbf{2}}\mathbf{+ \ }\mathbf{a}^{\mathbf{2}}}$ = $\frac{1}{a}$arctg$\frac{x}{a}$ + C 14. ʃ $\frac{\mathbf{\text{dx}}}{\mathbf{x}^{\mathbf{2}}\mathbf{-}\mathbf{a}^{\mathbf{2}}}$ = $\frac{1}{2a}$ln |$\frac{x - a}{x + a}$| + C 15. ʃ $\frac{\mathbf{\text{dx}}}{\sqrt{\mathbf{a}^{\mathbf{2}}\mathbf{-}\mathbf{x}^{\mathbf{2}}}}$ = arcsin$\frac{x}{a}$ + C 16. $\frac{\mathbf{\text{dx}}}{\sqrt{\mathbf{a}^{\mathbf{2}}\mathbf{+ q}}}$ = ln |x + $\sqrt{x^{2} + \ q}|\ $+ C

L = ʃ$\sqrt{1 + {\lbrack f^{'}\left( x \right)\rbrack}^{2}}$dx

V = πʃ[f²(x)]dx

V = πʃ[f²(x) - g²(x)]dx

Pp = 2πʃ f(x)$\sqrt{1 + \ {\lbrack f^{'}\left( x \right)\rbrack}^{2}}$dx

1.(C)’=0; 2.(xⁿ)’=nx^n-1; 3.(x)’=1; 4.($\frac{\mathbf{a}}{\mathbf{x}}$)’=-$\frac{a}{x^{2}}$; 5.($\sqrt{\mathbf{x}}$)’ = $\frac{1}{2\sqrt{x}}$ 6. (a^x)’=a^xln a 7. (e^x)’ = e^x 8. (log_ax)’ = $\frac{1}{\text{xlna}}$ 9. (lnx)’ = $\frac{1}{x}$ 10. (sinx)’ = cosx 11. (cosx)’ = -sinx 12. (tgx)’ = $\frac{1}{\cos^{2}x}$ 13. (ctgx)’ = - $\frac{1}{\sin^{2}x}$ 14. (arcsinx)’ = $\frac{1}{\sqrt{1 - \ x^{2}}}$ 15. (arccosx)’ = - $\frac{1}{\sqrt{1 - \ x^{2}}}$ 16. (arctgx)’ = $\frac{1}{x^{2} + 1}$ 17. (acctgx)’ = - $\frac{1}{x^{2} + 1}$