高等数学公式
导数公式:
(tgx)??sec2x(ctgx)???csc2x(secx)??secx?tgx(cscx)???cscx?ctgx(ax)??axlna
1
(logax)??
xlna
基本积分表:
(arcsinx)??
1
?x2
1
(arccosx)???
?x21
(arctgx)??
1?x2
1
(arcctgx)???
1?x2
?tgxdx??lncosx?C?ctgxdx?lnsinx?C
?secxdx?lnsecx?tgx?C?cscxdx?lncscx?ctgx?C
dx1x
?arctg?C?a2?x2aadx1x?a
?ln?x2?a22ax?a?Cdx1a?x
??a2?x22alna?x?Cdxx
?arcsin?C?a2?x2
a
?
2
n
dx2
?cos2x??secxdx?tgx?Cdx2
?sin2x??cscxdx??ctgx?C
?secx?tgxdx?secx?C?cscx?ctgxdx??cscx?C
ax
?adx?lna?C
x
?shxdx?chx?C?chxdx?shx?C?
dxx2?a2
?ln(x?x2?a2)?C
?
2
In??sinxdx??cosnxdx?
n?1
In?2n
???
x2a22
x?adx?x?a?ln(x?x2?a2)?C
22x2a2222
x?adx?x?a?lnx?x2?a2?C
22x2a2x222
a?xdx?a?x?arcsin?C
22a
2
2
三角函数的有理式积分:
2u1?u2x2du
sinx?, cosx?, u?tg, dx?
21?u21?u21?u2
一些初等函数: 两个重要极限:
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