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ViNT 13.04.2010 01:10

Èíòåãðàë sec(x)
 
Ïîÿâèëàñü íåîáõîäèìîñòü àíàëèòè÷åñêè âçÿòü îïðåäåëåííûé èíòåãðàë sec(x)dx, íàøåë â âèêèïåäèè, ÷òî îí ðàâåí ln|secx+tanx|.
Âîïðîñ: êàê âçÿòü òàêîé èíòåãðàë(ïîäçàáûë óæå èíòåãðèðîâàíèå òðèãîíîìåòðè÷åñêèõ ôóíêöèé)?

genroelgvozo 14.06.2010 21:51

Îòâåò: Èíòåãðàë sec(x)
 
íå çíàþ íà ñêîëüêî ýòî ñòàíäàðòíûé ñïîñîá íî äîñòàòî÷íî ýëåãàíòûé
sec(x)=1/cos(x)
sin(x)=t
cos(x)=sqrt(1-t^2)
x=arcsin(t)
dx=dt/sqrt(1-t^2)
çàìåíÿåøü è ïîëó÷àåòñÿ dt/(1-t^2)
íó à òóò óæå äëèèííûé ëîãàðèôì

genroelgvozo 14.06.2010 21:59

Îòâåò: Èíòåãðàë sec(x)
 
òîêà òàì èçíà÷àëüíî ïîëó÷èòñÿ íå òî ÷òî ó òåáÿ è äàæå íå ñîâñåì ïîõîæåå
íî åñëè ïðåîáðàçîâàòü òî âñå ïîëó÷àåòñÿ

Reizel 09.12.2010 23:09

Îòâåò: Èíòåãðàë sec(x)
 
Òîâàðèùè! Ïîìîãèòå! ×åìó ðàâíà ïåðâîîáðàçíàÿ îò 1/e ?

impersonalis 09.12.2010 23:29

Îòâåò: Èíòåãðàë sec(x)
 
x/e+C


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