| dx | ||
∫ | = | |
| 2x2−2x+5 |
| 1 | ||
przekształć do postaci ∫ | dx | |
| 1+x2 |
| √2 | √2 | |||
otrzymałam to : | arctg | (2x−1) +C ale chyba coś robię nie tak bo w Wolframie | ||
| 3 | 3 |
| √2 | 2x−1 | |||
ma byc 1/3 przed wszystkim a nie | a przy arctg | |||
| 3 | 3 |
| 1 | 1 | 1 | 1 | |||||
= | ∫ | dx= | ∫ | dx= | ||||
| 2 | x2−x+52 | 2 | (x−12)2−14+52 |
| 1 | 1 | |||
= | ∫ | dx=... | ||
| 2 | (x−12)2+94 |
| 1 | 3 | 3 | 2x−1 | |||||
[x− | = | t, dx= | dt, t= | ] | ||||
| 2 | 2 | 2 | 3 |
| 1 | 3 | 1 | ||||
= | * | ∫ | dt= | |||
| 2 | 2 | 94t2+94 |
| 3 | 4 | 1 | ||||
= | * | ∫ | dt= | |||
| 4 | 9 | t2+1 |
| 1 | 1 | 2x−1 | ||||
= | arctgt= | arctg | +C | |||
| 3 | 3 | 3 |
