| (2x+50)dx | ||
Obliczyć całkę nieoznaczoną ∫ | ||
| x2+10x+9 |
| 2x+10 | 1 | |||
∫ | dx+40∫ | dx | ||
| x2+10x+9 | x2+10x+9 |
| 1 | 1 | |||
A ∫ | dx można zapisać jako: ∫ | dx, x+5=t | ||
| x2+10x+9 | (x+5)2−16 |
| 1 | 1 | |||
∫ | dt=∫ | dt | ||
| t2−16 | (t−4)(t+4) |
| A | B | 1 | |||
+ | = | ||||
| t+4 | t−4 | (t−4)(t+4) |
| 1 | ||
B= | ||
| 8 |
| 1 | ||
A=− | ||
| 8 |
| 1 | 1 | 1 | 1 | 1 | ||||||
∫ | dt= | ∫ | dt− | ∫ | dt | |||||
| (t−4)(t+4) | 8 | t−4 | 8 | t+4 |