大一高数公式定理总结
摘要:大一高数公式定理总结导数公式(tgx) ??sec2x(arcsinx) ??1(ctgx)???csc2x?x2(secx)??secx?tgx(arccosx)???1(cscx)???cscx?ctgx?x2(ax)??axlna(arctgx)?...
大一高数公式定理总结
导数公式
(tgx) ??sec2x(arcsinx) ??1
(ctgx)???csc2x?x2
(secx)??secx?tgx(arccosx)???1
(cscx)???cscx?ctgx?x2(ax)??axlna(arctgx)??l
1?x2
(loglax)??
xlna
(arcctgx) ???l
1?x2
基本积分表
?tgxdx??1ncosx?CC??dxctgxdx?1nsinx?Ccos2x??sec2
xdx?tgx??secxdx?lnsecx?tgx?C?dx2sin2x??cscxdx??ctgx?C
?cscxdx?lncscx?ctgx?C
?secx?tgxdx?secx?C
?dx?cscx?ctgxdx??cscx?Ca2?x2?1aarctgx
a?C?dx1x??axdx ?ax
lna?C
x2?a2?2alna
x?a?C?shxdx?chx?C?dxa2?x2?1a?x2alna?x?C?chxdx?shx?C?dxa2?x2?arcsinx
a
?C?
dxx2?a2
?ln(x?x2?a2)?C?
?22
In
n??sinxdx??cosnxdx?
n?1
n
In?2?x2
?a2
dx?x22
a22x?a?21n(x?x2?a2)?C?x?adx?x22222
a2x?a?21nx?x2?a2?C?
a2?x2dx?x22
a2x2a?x?2arcsina
?C
三角函数的有理式积分
sinx?2u1?u2x2du
1?u2cosx?1?u2u?tg2,dx?1?u2
一些初等函数:两个重要极限
x?x
双曲正弦:shx?e?e2limsinxx?0x
?1chx?
ex?e?x
双曲余弦:2limx??(1?1
x
)x?e?..
双曲正切:thx?shxex?e?x
chx?ex
?e?xarshx?1n(x?x2?1) archx??1n (x?x2?1)arthx?11?x
2ln
1?x
三角函数公式:·诱导公式:·和差角公式:·和差化积公式
sin(???)?sin?cos??cos?sin?sin??sin??2sin???
cos (???)?cos?cos??sin?sin?2cos???
2tg(???)?tg??tg?
sin??sin??2cos??????1?tg??tg?2sin
2cos??cos??2cos??????ctg(???)?
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