| x2 | ||
∫ | * dx w mianowniku korzystam ze wzoru na a2 − b2 i otrzymuje | |
| 5−x6 |
| 1 | ||
∫ | ||
| (p5−t)(p5+t) |
| 1 | ||
Podstawiłem, ale mam ∫ | i nie wiem co dalej  masakra jakaś | |
| 5−t2 |
| x2dx |
| 1 | du | |||||||||||
∫ | = | = | ∫ | = J. | ||||||||||
| 5−x6 | 3 | 5−u2 |
| 1 | 1 | 1 | 1 | 1 | |||||
= | = | *( | + | ) | |||||
| 5−u2 | (√5−u)(√5+u) | 2√5 | √5−u | √5+u |
| 1 | 1 | 1 | 1 | |||||
J = | * | *∫( | + | )du = | ||||
| 3 | 2√5 | √5−u | √5+u |
| √5 | √5 | √5+u | ||||
= | *(−ln|√5−u| + ln|√5+u|) + c = | *ln| | | + c = | |||
| 30 | 30 | √5−u |
| √5 | √5+x3 | |||
= | *ln| | | + c. | ||
| 30 | √5−x3 |
