| 1−x | dx | (1−x2)12 | dx | |||||
∫( | )12 * | = ∫ | * | = | ||||
| 1+x | x | 1+x | x |
| dt | u | |||
|x = sint,dx = costdt| = ∫ | = | | = | ||
| sin2t+sint | 2 |
| u | 2udu | 2u | 1−u2 | |||||
arctgt,t=tg | ,dt= | ,sint = | ,cost = | | | ||||
| 2 | u2+1 | u2+1 | u2+1 |
| u4+2u3+2 | u3 | u | 1 | |||||
= .. = ∫ | du = | + | − | =... no i wstawic | ||||
| 4u2 | 12 | 2 | 2u |
| 1−x | 1−t2 | |||
A może po prostu podstawić t2 = | ? x= | |||
| 1+x | 1+t2 |
| t2 | 1−t | |||
Całka = −4 ∫ | dt = 2 arctg t − ln | |||
| (1−t2)(1+t2) | 1+t |