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(???)?