| 1 | t2+1−t2 | |||
∫ | dt=∫ | dt= | ||
| (1+t2)2 | (1+t2)2 |
| 1 | t | |||
=∫ | dt−∫t* | dt= | ||
| (1+t2) | (1+t2)2 |
| 1 | ||
J1=∫ | dt =arctgt | |
| 1+t2 |
| t | ||
J2=∫t* | dt = | |
| (1+t2)2 |
| t | t | |||
[t=u, dt =du, dv= | dt, v=∫ | dt, podstawienie 1+t2=s, 2tdt=ds, | ||
| (1+t2)2 | (1+t2)2 |
| 1 | 1 | 1 | 1 | |||||
v= | ∫ | ds= | *(−1)s−1=− | ] | ||||
| 2 | s2 | 2 | 2(1+t2) |
| 1 | 1 | 1 | ||||
J2=t*− | + | ∫ | dt= | |||
| 2(1+t2) | 2 | 1+t2 |
| t | 1 | |||
=− | + | arctgt | ||
| 2(1+t2) | 2 |
| 1 | 1 | t | ||||
∫ | dt = | arctg(t)+ | ||||
| (1+t2)2 | 2 | 2(1+t2) |
| 5^2 | 52 |
| 2^{10} | 210 |
| a_2 | a2 |
| a_{25} | a25 |
| p{2} | √2 |
| p{81} | √81 |
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