| dx | ||
całka ∫ | ||
| ex−e−x |
| dx | dx | exdx | |||||||||||||||||||
∫ | = ∫ | = ∫ | =
| ||||||||||||||||||
|
| e2x − 1 |
| ⎧ | ex = t | ||
| = | ⎩ | dt = exdx | = |
| dt | ||
= ∫ | = ... | |
| t2 − 1 |
,
bo ja widzę to np. tak :
| dx | exdx | dt | ||||
... = ∫ | =∫ | = |ex=t ⇒ exdx=dt ⇒ dx= | | = | |||
| e−x(e2x−1) | (ex)2−1 | t |
| tdt | dt | 1 | dt | dt | 1 | t−1 | ||||||||
= ∫ | =∫ | = | (∫ | −∫ | )= | ln| | |= | |||||||
| t(t2−1) | (t−1)(t+1) | 2 | t−1 | t+1 | 2 | t+1 |
| 1 | ex−1 | |||
= | ln| | | +C . ...  | ||
| 2 | ex+1 |