d()=2dx d()=costdt [img=95x35]17e0c406449d63e.jpg[/img]
d()=2dx d()=costdt [img=95x35]17e0c406449d63e.jpg[/img]
在求[img=86x37]17da5ab996bf530.jpg[/img]时，可设x=sint,dx=costdt
在求[img=86x37]17da5ab996bf530.jpg[/img]时，可设x=sint,dx=costdt
【简答题】请问各位数学天才关于∫(arcsinx)²dx=?的这两种做法都正确吗令t=arcsinx,则x=sint,dx=costdt∫(arcsinx)²dx=∫t²·costdt=t²·sint-∫2t·sintdt=t²·sint+∫2t·d(cost)=t²·sint+2tcost-∫2costdt=t²·sint+2tcost-2sint+C=x·arcsin²x+2arcsinx·√
【简答题】请问各位数学天才关于∫(arcsinx)²dx=?的这两种做法都正确吗令t=arcsinx,则x=sint,dx=costdt∫(arcsinx)²dx=∫t²·costdt=t²·sint-∫2t·sintdt=t²·sint+∫2t·d(cost)=t²·sint+2tcost-∫2costdt=t²·sint+2tcost-2sint+C=x·arcsin²x+2arcsinx·√
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