| dt | dt | |||
1 + ex = t , exdx = dt , dx = | = | |||
| ex | t − 1 |
| dt | t2 − 1 + 1 | (t − 1)*(t + 1) + 1 | ||||
J = ∫t2* | = ∫ | dt = ∫ | dt | |||
| t − 1 | t − 1 | t − 1 |
| 1 | 1 | |||
J = ∫(t + 1 + | )dt = | *t2 + t + ln(t − 1) | ||
| t − 1 | 2 |
| 1 | ||
J = | *(1 + ex)2 + 1 + ex + ln(1 + ex − 1) | |
| 2 |
| 1 | ||
J = | *(1 + ex)2 + 1 + ex + ln(ex) | |
| 2 |
| 1 | ||
J = | (1 + ex)2 + ex + x + 1 + C | |
| 2 |