| 1 | sin2x+cos2x | cos2x | ||||
1. ∫ | dx = ∫ | dx = ∫sinx dx + ∫ | .... | |||
| sinx | sinx | sinx |
| cos2x | ||
Nie wiem jak obliczyć tę ∫ | ||
| sinx |
| 1 | sin(x) | sin(x) | ||||
∫ | = ∫ | = ∫ | = | |||
| sin(x) | sin2(x) | 1 − cos2(x) |
| dt | 1 | 1 | 1 | 1 | ||||||
= ∫ | = | ∫ | − | ∫ | = | |||||
| t2 − 1 | 2 | t − 1 | 2 | t + 1 |
| 1 | 1 | 1 | t − 1 | ||||
ln|t − 1| − | ln|t + 1| +C = | ln| | | + C = | ||||
| 2 | 2 | 2 | t + 1 |
| 1 | cos(x) − 1 | ||
ln| | | + C | ||
| 2 | cos(x) + 1 |
| 1 | 1 | |||
= ∫ −t5(1 − t2)dt = ∫ t7dt − ∫ t5dt = | t8 − | t6 + C = | ||
| 8 | 6 |
| 1 | 1 | ||
cos8(x) − | cos6(x) + C | ||
| 8 | 6 |
I − łeś. 