| arctg( x + a ) | ||
Oblicz ∫0 + ∞ | dx , a−ustalona liczba | |
| 1 + x2 |
| arctan(x+a) | ||
g(a) = ∫0∞ | dx | |
| 1+x2 |
| arctan((x+h)+a)−arctan(x+a) | 1 | ||
= | gdzie y jest pomiędzy x, x+h | ||
| h | 1+(y+a)2 |
| 1 | |||||||||
g'(a) = ∫0∞ | dx = ∫0∞ | dx | ||||||||
| 1+x2 | (1+x2)(1+(x+a)2) |
| ln(a2+1)+a*arctan(a) | 1 | |||
= − | +π | |||
| a3+4a | a2+4 |
| π2 | π | ln(x2+1)+x*arctan(x) | |||
+ | arctan(a/2) − ∫0a | dx | |||
| 8 | 2 | x3+4x |