| 1 | ||
dt= | dx | |
| 2√x |
| 1 | ||
dt= | dx | |
| 2t |
| 1 | 1 | t3 | ||||
..=2∫t2arctg(t)dt=2( | t3arctg(t)− | ∫ | dt) | |||
| 3 | 3 | t2+1 |
| t3 | t(t2+1) | t | 1 | 1 | ||||||
∫ | dt)=∫ | dt−∫ | dt= | t2− | ln|t2+1|+C | |||||
| t2+1 | t2+1 | t2+1 | 2 | 2 |
| 1 | ||
2∫t2arctg(t)dt= | (2t3arctg(t)−t2+ln|t2+1|)+C | |
| 3 |
| 1 | ||
...= | (2√x3arctg√x−x+ln|x+1|)+C | |
| 3 |
| 2 | 2 | 1 | 1 | ||||
∫√xarctg(√x)dx= | x√xarctg(√x)− | ∫x√x | dx | ||||
| 3 | 3 | 2√x | 1+x |
| 2 | 1 | x | ||||
∫√xarctg(√x)dx= | x√xarctg(√x)− | ∫ | dx | |||
| 3 | 3 | 1+x |
| 2 | 1 | x+1−1 | ||||
∫√xarctg(√x)dx= | x√xarctg(√x)− | ∫ | dx | |||
| 3 | 3 | 1+x |
| 2 | 1 | 1 | 1 | |||||
∫√xarctg(√x)dx= | x√xarctg(√x)− | ∫dx+ | ∫ | dx | ||||
| 3 | 3 | 3 | 1+x |
| 2 | 1 | 1 | ||||
∫√xarctg(√x)dx= | x√xarctg(√x)− | x+ | ln|1+x|+C | |||
| 3 | 3 | 3 |