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Ò»Íë°×¿ªË®: ½ð±Ò+10 2015-07-25 15:49:01
Õâ¸ö¿ÉÏȰ´·Ö²½»ý·Ö·¨½«Integral{exp(-a*x)*sin(b*x)*dx}Çó³ö²»¶¨»ý·Ö£¬È»ºó½«ÉÏÏÂÏÞ´úÈëµÃµ½½á¹û¡£×îºóÔÙÀûÓÃÅ·À­¹«Ê½½øÐе¥±äÁ¿¸´±äº¯ÊýµÄ»¯¼ò¼´¿É¡£ÆäÖеIJ»¶¨»ý·Ö¼ÆËãÈçÏ£º
Integral{exp(-a*x)*sin(b*x)*dx}
=-1/b*Integral{exp(-a*x)*dCos(b*x)}
=-1/b*exp(-a*x)*Cos(b*x)-a/b*Integral{exp(-a*x)*Cos(b*x)*dx}
=-1/b*exp(-a*x)*Cos(b*x)-a/b^2*Integral{exp(-a*x)*dSin(b*x)}
=-1/b*exp(-a*x)*Cos(b*x)-a/b^2*exp(-a*x)*Sin(b*x)-(a/b)^2*Integral{exp(-a*x)*sin(b*x)*dx}
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Integral{exp(-a*x)*sin(b*x)*dx}
=[-1/b*exp(-a*x)*Cos(b*x)-a/b^2*exp(-a*x)*Sin(b*x)]/[1+(a/b)^2]
=-[b*exp(-a*x)*Cos(b*x) + a*exp(-a*x)*Sin(b*x)]/(a^2+b^2)
2Â¥2015-07-25 08:46:27
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2Â¥: Originally posted by peterflyer at 2015-07-25 08:46:27
Õâ¸ö¿ÉÏȰ´·Ö²½»ý·Ö·¨½«Integral{exp(-a*x)*sin(b*x)*dx}Çó³ö²»¶¨»ý·Ö£¬È»ºó½«ÉÏÏÂÏÞ´úÈëµÃµ½½á¹û¡£×îºóÔÙÀûÓÃÅ·À­¹«Ê½½øÐе¥±äÁ¿¸´±äº¯ÊýµÄ»¯¼ò¼´¿É¡£ÆäÖеIJ»¶¨»ý·Ö¼ÆËãÈçÏ£º
Integral{exp(-a*x)*sin(b*x)*dx}
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