| dx | ||
a) ∫ | ||
| 1+4x2 |
| x | ||
b) ∫ | ||
| cos2x |
| 1 | 1 | ||
= | |||
| 1+4x2 | 1+(2x)2 |
| dt | ||
dx = | ||
| 2 |
| 1 | dt | 1 | 1 | 1 | |||||
J = ∫ | = | ∫ | dt = | arctgt+C = | |||||
| 1+t2 | 2 | 2 | 1+t2 | 2 |
| 1 | |
arctg(2x)+C | |
| 2 |
| 1 | ||
g'(x)= | g(x) = tgx | |
| cos2x |
| sinx | ||
J = x*tgx − ∫tgx dx = x*tgx − ∫ | dx | |
| cosx |
| −dt | ||
J = x*tgx −∫ | = x*tgx + ln|t|+C = x*tgx+ln|cosx|+C | |
| t |
| dx | ||
∫ | miałem takie na kolokwium, i do tej pory nie wiem jak to zrobić.... | |
| √8−4x2 |
| dx | ||
i takiej: ∫ | taką też miałem...  | |
| 3+4x2 |
| x | ||
t = | ||
| √2 |
| 2x | ||
3+4x2 = 3(1+43x2) = 3(1+( | )2) | |
| √3 |
| 2 | ||
t = | x | |
| √3 |