4积分换元技巧 f(at+b)de f(at+b d(at+b) f(x) d=2f(√x)d(√x) f(at' +b)dx f(at'+b) d(at+ 2b)( (In x) dx= f(n x)d(nx 2a sT /(a)adr=f(ay d(a2) f(e e d=f(e d(e) n a f(sin x)cos xdx=f(sin x)d (sin x) f(shr)ch xdx=f(shx)d(shx) f(tan xsec xdx= f(tan xd(tan x) (3)-=( trades 丰m9换x1 王三角代换 x=aint 双曲代换x=asht 高等数学(XJD) ▲u高等数学（XJD） 2 ( ) ( ) ( ) dx f x d x x f x = (ln ) (ln ) (ln ) dx f x d x x f x =              = −      x d x dx f x x f 1 1 1 1 2 f (sin x)cos xdx = f (sin x)d(sin x) ( ) ln ( ) ( ) x x x x d a a f a f a a dx = (tan )sec (tan ) (tan ) 2 f x xdx = f x d x (arctan ) (arctan ) 1 (arctan ) 2 dx f x d x x f x = + ( ) ( ) ( ) d at b a f at b f at b dx + + + = ( ) 2 ( ) ( ) 2 2 2 d at b a f at b f at b dx + + + = f (sh x)ch xdx = f (sh x)d(sh x) 4. 积分换元技巧 三角代换x = asint 双曲代换x = asht t x 1 倒置代换 = ( ) ( ) ( ) x x x x f e e dx = f e d e