| 1 | ||
u = arctg(x) , u' = | ||
| x2 + 1 |
| 2 | ||
v' = 2x2 , v = | x3 | |
| 3 |
| 2 | 2 | x3 | |||
∫2x2arctgx dx = | x3arctg(x) − ∫ | dx | |||
| 3 | 3 | x2 + 1 |
| 1 | x3 | |||
∫2x2arctan(x) dx = 2∫x2arctan(x) = [u=arctan(x) dv=x2dx du= | v= | ] | ||
| 1+x2 | 3 |
| 2 | x3 + x − x | ||
∫ | dx = | ||
| 3 | x2 + 1 |
| 1 | x(x2 + 1) | 1 | 2x | |||||
= | ∫2 | dx + | ∫ | dx = ... | ||||
| 3 | x2 + 1 | 3 | x2 + 1 |
| 5^2 | 52 |
| 2^{10} | 210 |
| a_2 | a2 |
| a_{25} | a25 |
| p{2} | √2 |
| p{81} | √81 |
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