| 4ex | ||
∫0 +∞ | dx | |
| e2x−4ex+5 |
| ex | ||
funkcja pod całką = | ||
| (ex−2)2+1 |
| 4ex | ex | |||
∫ | dx = 4 ∫ | dx = ... | ||
| e2x−4ex+5 | (ex)2−4ex+5 |
| 1 | 1 | |||
... = 4 ∫ | dt = 4 ∫ | dt = 4*arctg(t−2) + C = 4arctg(ex−2)+C | ||
| t2−4t+5 | (t−2)2+1 |
| 4ex | 4ex | |||
∫0+∞ | dx = ∫0A | dx = | ||
| e2x−4ex+5 | e2x−4ex+5 |
| π | ||
= limA→+∞ 4arctg(eA−2) − 4arctg(e0−2) = 4arctg(+∞} − 4arctg(1−2) = 4* | − 4arctg(−1) | |
| 2 |
| π | ||
= 2π − 4*(− | ) = 3π | |
| 4 |