∫dx = x + c

$$\int_{}^{}{x^{n}\ dx = \frac{x^{n + 1}}{n + 1}} + c$$

$$\int_{}^{}{\frac{1}{x}\ dx = \ln\left| x \right|} + c$$

$$\int_{}^{}{a^{x}\ dx = \frac{a^{x}}{\ln a}} + c$$

∫e^x dx = e^x + c

$$\int_{}^{}{e^{\text{ax}}\ dx =}\frac{1}{a}e^{\text{ax}} + c$$

∫sinax dx = -cosax + c

∫cosax dx = sinax + c

∫tgx dx = −ln|cosx| + c

∫ctgx dx=ln|sinx| + c

$$\int_{}^{}{\frac{\text{dx}}{\operatorname{}x}\ = \operatorname{-ctg}x} + c$$

$$\int_{}^{}{\frac{\text{dx}}{\operatorname{}x}\ = \operatorname{tg}x} + c$$

$$\int_{}^{}{\frac{\text{dx}}{x^{2} + a^{2}} =}\frac{1}{a}\operatorname{arc\ tg}\frac{x}{a} + c$$

$$\int_{}^{}{\frac{\text{dx}}{x^{2} - a^{2}} =}\frac{1}{2a}\ln\left| \left. \ \frac{x - a}{x + a} \right| \right.\ + c$$

$$\int_{}^{}{\frac{\text{dx}}{\sqrt{a^{2} - x^{2}}} =}\operatorname{arc\ sin}\frac{x}{a} + c$$

$$\int_{}^{}{\frac{\text{dx}}{\sqrt{x^{2} + q}} =}\ln\left| x + \right.\ \left. \ \sqrt{x^{2} + q} \right| + c$$

∫[f(x)+g(x)]dx=∫f(x)dx+∫g(x)dx

∫[f(x)-g(x)]dx=∫f(x)dx-∫g(x)dx

∫af(x)dx = a∫f(x)dx

cos2x = cos²x − sin²x

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab + b²

1. (C)’ = 0

2. (xⁿ)′ = nx^n − 1

3. (x)’ = 1

4. ($\frac{a}{x})' = \ - \ \frac{a}{x^{2}}$

5. ($\sqrt{x)}$’ = $\frac{1}{2\sqrt{x}}$

6. (a^x)^′ =  a^xlna

7. (e^x)′ =  e^x

8. $\left( \log_{a}x \right)^{'} = \ \frac{1}{\text{xlna}}$

9. $\left( \text{lnx} \right)^{'} = \ \frac{1}{x}$

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. (arccos)’ = -$\frac{1}{\sqrt{1 - x^{2}}}$

16. (arctgx)’ = $\frac{1}{x^{2} + 1}$

17. (arcctgx)’ = - $\frac{1}{x^{2} + 1}$

[F(x)*g(x)]’=f’(x)g(x)+f(x)g’(x)

$$(\sqrt{})' = \frac{1}{2\sqrt{}}*^{2}$$

(²)^′ = 2 * *’

∫dx = x + c

$$\int_{}^{}{x^{n}\ dx = \frac{x^{n + 1}}{n + 1}} + c$$

$$\int_{}^{}{\frac{1}{x}\ dx = \ln\left| x \right|} + c$$

$$\int_{}^{}{a^{x}\ dx = \frac{a^{x}}{\ln a}} + c$$

∫e^x dx = e^x + c

$$\int_{}^{}{e^{\text{ax}}\ dx =}\frac{1}{a}e^{\text{ax}} + c$$

∫sinax dx = -cosax + c

∫cosax dx = sinax + c

∫tgx dx = −ln|cosx| + c

∫ctgx dx=ln|sinx| + c

$$\int_{}^{}{\frac{\text{dx}}{\operatorname{}x}\ = \operatorname{-ctg}x} + c$$

$$\int_{}^{}{\frac{\text{dx}}{\operatorname{}x}\ = \operatorname{tg}x} + c$$

$$\int_{}^{}{\frac{\text{dx}}{x^{2} + a^{2}} =}\frac{1}{a}\operatorname{arc\ tg}\frac{x}{a} + c$$

$$\int_{}^{}{\frac{\text{dx}}{x^{2} - a^{2}} =}\frac{1}{2a}\ln\left| \left. \ \frac{x - a}{x + a} \right| \right.\ + c$$

$$\int_{}^{}{\frac{\text{dx}}{\sqrt{a^{2} - x^{2}}} =}\operatorname{arc\ sin}\frac{x}{a} + c$$

$$\int_{}^{}{\frac{\text{dx}}{\sqrt{x^{2} + q}} =}\ln\left| x + \right.\ \left. \ \sqrt{x^{2} + q} \right| + c$$

∫[f(x)+g(x)]dx=∫f(x)dx+∫g(x)dx

∫[f(x)-g(x)]dx=∫f(x)dx-∫g(x)dx

∫af(x)dx = a∫f(x)dx

cos2x = cos²x − sin²x

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab + b²

1. (C)’ = 0

2. (xⁿ)′ = nx^n − 1

3. (x)’ = 1

4. ($\frac{a}{x})' = \ - \ \frac{a}{x^{2}}$

5. ($\sqrt{x)}$’ = $\frac{1}{2\sqrt{x}}$

6. (a^x)^′ =  a^xlna

7. (e^x)′ =  e^x

8. $\left( \log_{a}x \right)^{'} = \ \frac{1}{\text{xlna}}$

9. $\left( \text{lnx} \right)^{'} = \ \frac{1}{x}$

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. (arccos)’ = -$\frac{1}{\sqrt{1 - x^{2}}}$

16. (arctgx)’ = $\frac{1}{x^{2} + 1}$

17. (arcctgx)’ = - $\frac{1}{x^{2} + 1}$

[F(x)*g(x)]’=f’(x)g(x)+f(x)g’(x)

$$(\sqrt{})' = \frac{1}{2\sqrt{}}*^{2}$$

(²)^′ = 2 * *’

∫dx = x + c

$$\int_{}^{}{x^{n}\ dx = \frac{x^{n + 1}}{n + 1}} + c$$

$$\int_{}^{}{\frac{1}{x}\ dx = \ln\left| x \right|} + c$$

$$\int_{}^{}{a^{x}\ dx = \frac{a^{x}}{\ln a}} + c$$

∫e^x dx = e^x + c

$$\int_{}^{}{e^{\text{ax}}\ dx =}\frac{1}{a}e^{\text{ax}} + c$$

∫sinax dx = -cosax + c

∫cosax dx = sinax + c

∫tgx dx = −ln|cosx| + c

∫ctgx dx=ln|sinx| + c

$$\int_{}^{}{\frac{\text{dx}}{\operatorname{}x}\ = \operatorname{-ctg}x} + c$$

$$\int_{}^{}{\frac{\text{dx}}{\operatorname{}x}\ = \operatorname{tg}x} + c$$

$$\int_{}^{}{\frac{\text{dx}}{x^{2} + a^{2}} =}\frac{1}{a}\operatorname{arc\ tg}\frac{x}{a} + c$$

$$\int_{}^{}{\frac{\text{dx}}{x^{2} - a^{2}} =}\frac{1}{2a}\ln\left| \left. \ \frac{x - a}{x + a} \right| \right.\ + c$$

$$\int_{}^{}{\frac{\text{dx}}{\sqrt{a^{2} - x^{2}}} =}\operatorname{arc\ sin}\frac{x}{a} + c$$

$$\int_{}^{}{\frac{\text{dx}}{\sqrt{x^{2} + q}} =}\ln\left| x + \right.\ \left. \ \sqrt{x^{2} + q} \right| + c$$

∫[f(x)+g(x)]dx=∫f(x)dx+∫g(x)dx

∫[f(x)-g(x)]dx=∫f(x)dx-∫g(x)dx

∫af(x)dx = a∫f(x)dx

cos2x = cos²x − sin²x

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab + b²

1. (C)’ = 0

2. (xⁿ)′ = nx^n − 1

3. (x)’ = 1

4. ($\frac{a}{x})' = \ - \ \frac{a}{x^{2}}$

5. ($\sqrt{x)}$’ = $\frac{1}{2\sqrt{x}}$

6. (a^x)^′ =  a^xlna

7. (e^x)′ =  e^x

8. $\left( \log_{a}x \right)^{'} = \ \frac{1}{\text{xlna}}$

9. $\left( \text{lnx} \right)^{'} = \ \frac{1}{x}$

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. (arccos)’ = -$\frac{1}{\sqrt{1 - x^{2}}}$

16. (arctgx)’ = $\frac{1}{x^{2} + 1}$

17. (arcctgx)’ = - $\frac{1}{x^{2} + 1}$

[F(x)*g(x)]’=f’(x)g(x)+f(x)g’(x)

$$(\sqrt{})' = \frac{1}{2\sqrt{}}*^{2}$$

(²)^′ = 2 * *’

∫dx = x + c

$$\int_{}^{}{x^{n}\ dx = \frac{x^{n + 1}}{n + 1}} + c$$

$$\int_{}^{}{\frac{1}{x}\ dx = \ln\left| x \right|} + c$$

$$\int_{}^{}{a^{x}\ dx = \frac{a^{x}}{\ln a}} + c$$

∫e^x dx = e^x + c

$$\int_{}^{}{e^{\text{ax}}\ dx =}\frac{1}{a}e^{\text{ax}} + c$$

∫sinax dx = -cosax + c

∫cosax dx = sinax + c

∫tgx dx = −ln|cosx| + c

∫ctgx dx=ln|sinx| + c

$$\int_{}^{}{\frac{\text{dx}}{\operatorname{}x}\ = \operatorname{-ctg}x} + c$$

$$\int_{}^{}{\frac{\text{dx}}{\operatorname{}x}\ = \operatorname{tg}x} + c$$

$$\int_{}^{}{\frac{\text{dx}}{x^{2} + a^{2}} =}\frac{1}{a}\operatorname{arc\ tg}\frac{x}{a} + c$$

$$\int_{}^{}{\frac{\text{dx}}{x^{2} - a^{2}} =}\frac{1}{2a}\ln\left| \left. \ \frac{x - a}{x + a} \right| \right.\ + c$$

$$\int_{}^{}{\frac{\text{dx}}{\sqrt{a^{2} - x^{2}}} =}\operatorname{arc\ sin}\frac{x}{a} + c$$

$$\int_{}^{}{\frac{\text{dx}}{\sqrt{x^{2} + q}} =}\ln\left| x + \right.\ \left. \ \sqrt{x^{2} + q} \right| + c$$

∫[f(x)+g(x)]dx=∫f(x)dx+∫g(x)dx

∫[f(x)-g(x)]dx=∫f(x)dx-∫g(x)dx

∫af(x)dx = a∫f(x)dx

cos2x = cos²x − sin²x

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab + b²

1. (C)’ = 0

2. (xⁿ)′ = nx^n − 1

3. (x)’ = 1

4. ($\frac{a}{x})' = \ - \ \frac{a}{x^{2}}$

5. ($\sqrt{x)}$’ = $\frac{1}{2\sqrt{x}}$

6. (a^x)^′ =  a^xlna

7. (e^x)′ =  e^x

8. $\left( \log_{a}x \right)^{'} = \ \frac{1}{\text{xlna}}$

9. $\left( \text{lnx} \right)^{'} = \ \frac{1}{x}$

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. (arccos)’ = -$\frac{1}{\sqrt{1 - x^{2}}}$

16. (arctgx)’ = $\frac{1}{x^{2} + 1}$

17. (arcctgx)’ = - $\frac{1}{x^{2} + 1}$

[F(x)*g(x)]’=f’(x)g(x)+f(x)g’(x)

$$(\sqrt{})' = \frac{1}{2\sqrt{}}*^{2}$$

(²)^′ = 2 * *’

∫dx = x + c

$$\int_{}^{}{x^{n}\ dx = \frac{x^{n + 1}}{n + 1}} + c$$

$$\int_{}^{}{\frac{1}{x}\ dx = \ln\left| x \right|} + c$$

$$\int_{}^{}{a^{x}\ dx = \frac{a^{x}}{\ln a}} + c$$

∫e^x dx = e^x + c

$$\int_{}^{}{e^{\text{ax}}\ dx =}\frac{1}{a}e^{\text{ax}} + c$$

∫sinax dx = -cosax + c

∫cosax dx = sinax + c

∫tgx dx = −ln|cosx| + c

∫ctgx dx=ln|sinx| + c

$$\int_{}^{}{\frac{\text{dx}}{\operatorname{}x}\ = \operatorname{-ctg}x} + c$$

$$\int_{}^{}{\frac{\text{dx}}{\operatorname{}x}\ = \operatorname{tg}x} + c$$

$$\int_{}^{}{\frac{\text{dx}}{x^{2} + a^{2}} =}\frac{1}{a}\operatorname{arc\ tg}\frac{x}{a} + c$$

$$\int_{}^{}{\frac{\text{dx}}{x^{2} - a^{2}} =}\frac{1}{2a}\ln\left| \left. \ \frac{x - a}{x + a} \right| \right.\ + c$$

$$\int_{}^{}{\frac{\text{dx}}{\sqrt{a^{2} - x^{2}}} =}\operatorname{arc\ sin}\frac{x}{a} + c$$

$$\int_{}^{}{\frac{\text{dx}}{\sqrt{x^{2} + q}} =}\ln\left| x + \right.\ \left. \ \sqrt{x^{2} + q} \right| + c$$

∫[f(x)+g(x)]dx=∫f(x)dx+∫g(x)dx

∫[f(x)-g(x)]dx=∫f(x)dx-∫g(x)dx

∫af(x)dx = a∫f(x)dx

cos2x = cos²x − sin²x

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab + b²

1. (C)’ = 0

2. (xⁿ)′ = nx^n − 1

3. (x)’ = 1

4. ($\frac{a}{x})' = \ - \ \frac{a}{x^{2}}$

5. ($\sqrt{x)}$’ = $\frac{1}{2\sqrt{x}}$

6. (a^x)^′ =  a^xlna

7. (e^x)′ =  e^x

8. $\left( \log_{a}x \right)^{'} = \ \frac{1}{\text{xlna}}$

9. $\left( \text{lnx} \right)^{'} = \ \frac{1}{x}$

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. (arccos)’ = -$\frac{1}{\sqrt{1 - x^{2}}}$

16. (arctgx)’ = $\frac{1}{x^{2} + 1}$

17. (arcctgx)’ = - $\frac{1}{x^{2} + 1}$

[F(x)*g(x)]’=f’(x)g(x)+f(x)g’(x)

$$(\sqrt{})' = \frac{1}{2\sqrt{}}*^{2}$$

(²)^′ = 2 * *’