Pomocy
| e3x | ||
a) ∫ | dx | |
| 1−e6x |
| e√x | ||
b) ∫ | ||
| √x |
| sinxdx | ||
c) | ||
| 3+2cosx |
| 1 | ||
e3xdx = | dt
| |
| 3 |
| 1 | 1 | 1 | 1 | ||||
∫ | dt = | ∫ | dt =
| ||||
| 3 | 1 − t2 | 3 | (1 − t)(1 + t) |
| 1 | 1 | 1 | ||||
= | (∫ | dt + ∫ | dt) = ...
| |||
| 6 | 1 − t | 1 + t |
| 1 | 1 | |||
b) √x = t , | dx = dt, | dx = dt
| ||
| 2√x | √x |
| 1 | ||
c) 3 + 2cosx = t ⇒ −2sinxdx = dt ⇒ sinxdx = − | dt | |
| 2 |