pigor: ..., pisz duże U {...}{...} , a tak , jeśli o to chodzi :
| | arcsinx | | costdt | |
∫ |
| dx= | arcsinx=t ⇒ x=sint, dx=costdt |= ∫t* |
| = |
| | √1−x | | √1−sinx | |
| | costdt | | costdt | |
= |u= t, to du=dt i dv= |
| , to v= ∫ |
| = |niech |
| | √1−sint | | √1−sint | |
| | −2sds | |
√1−sint=s ⇒ 1−sint=s2 ⇒ −costdt=2sds |= ∫ |
| = −2∫ds= −2s= −2√1−sint= |
| | s | |
= −2t
√1−sint+2∫(1−sint)dt= −2t
√1−sint+2∫dt−2∫sintdt= −2t
√1−sint+2t+2cost=
= 2(t+cost−t
√1−sint)= 2(arcsinx+cos(arcsinx)−arcsinx
√1−sin(arcsinx)=
= 2(arcsinx+
√1−x2−arcsinx*
√1−x)=
2(√1−x2+(1−√1−x)arcsinx) +C=....
