| x2sin(√x3) | ||
Obliczyć całkę ∫ | dx | |
| √x3 |
| 1 | sin(√u) | 2 | |||
∫ | du = − | cos(√u) + C | |||
| 3 | √u | 3 |
| x2sin(√x3) | ||
∫ | dx = | |
| √x3 |
| ⎧ | t = x3 | ||
| = | ⎨ | dt = 3x2dx | = |
| ⎩ | dx = dt/3x2 |
| x2sin(√t) | 1 | 1 | sin(√t) | ||||
= ∫ | dt = | ∫ | dt = | ||||
| √t | 3x2 | 3 | √t |
| ⎧ | u = √t | ||
| ⎜ | du = 1/2√tdt | ||
| = | ⎨ | du = 1/2udt | = |
| ⎩ | dt = 2udu |
| 1 | sin(u) | 2 | ||||
= | ∫ | 2udu = | ∫sin(u)du = | |||
| 3 | u | 3 |
| 2 | 2 | |||
= − | cos(u) + C = − | cos(√x3) + C | ||
| 3 | 3 |
| sin(√x) | |
= [−2cos(√x)]'. | |
| √x |