| √x | ||
∫ | ||
| x+3 |
| √x | 1 | |||
∫ | dx={√x=t, x=t2, | dx=dt} | ||
| x+3 | 2√x |
| t | 2t2 | |||
=∫ | *2tdt=∫ | dt | ||
| t2+3 | t2+3 |
| t2+3−3 | ||
=2∫ | dt | |
| t2+3 |
| 1 | ||
=2(∫1dt−3∫ | dt) | |
| t2+3 |
| t | ||
=2(t−3arctg( | )/√3) | |
| √3 |
| √x | ||
=2(√x−3arctg( | )/√3) | |
| √3 |
| 1 | ||
∫ | dt | |
| t2+3 |
| 1 | 1 | 1 | ||||
∫ | dt= | ∫ | dt={t/√3=s, dt=√3ds} | |||
| t2+3 | 3 | (t/√3)2+1 |
| 1 | 1 | |||
= | ∫ | √3ds | ||
| 3 | s2+1 |
| √3 | 1 | |||
= | ∫ | ds | ||
| 3 | s2+1 |
| 1 | ||
= | arctg(s) | |
| √3 |
| 1 | ||
= | artcg(t/√3) | |
| √3 |
| 1 | 1 | √3 | 1 | |||||
∫ | dt=|t=s√3, dt=√3ds|=√3∫ | ds= | ∫ | ds=... | ||||
| t2+3 | 3s2+3 | 3 | s2+1 |
| 5^2 | 52 |
| 2^{10} | 210 |
| a_2 | a2 |
| a_{25} | a25 |
| p{2} | √2 |
| p{81} | √81 |
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