导数公式 (tgx)'=sec (arcsin x)=.I (ctx) (secx)=secx·t (arccos) (cscx)'=-cScx ctx (a)=a Ina 1+x (log。x) (arcctgx)=- ln 基本积分表: jtgxdx=-Inlcos x[+C sec xdx= tgx+C cos x 「 ctex= Inlsin x+C =csc xdx=-ctgx+C sec xdx=In sec x+tgx+C sin x csc xdx= Ncsc x-ctgx +C texdx arct -+C a dx=-+C d x a+x In a2-x2 2a a-x chxdx= shx +C =arcsin -+C n(x+√ I sin"xdx= cos"xdr=n-1 +a2)+C a-+ JVa2-x'dr=3Va2-x2+g-arcsin +C 三角函数的有理式积分: sInx= - cOSx= 1+ 2’a。2d 1+t导数公式： 基本积分表： 三角函数的有理式积分： 2 2 2 2 1 2 1 2 1 cos 1 2 sin u du dx x u tg u u x u u x + = = + − = + = ， ， ， x a x a a a x x ctgx x x tgx ctgx x tgx x a x x ln 1 (log ) ( ) ln (csc ) csc (sec ) sec ( ) csc ( ) sec 2 2 ′ = ′ = ′ = − ⋅ ′ = ⋅ ′ = − ′ = 2 2 2 2 1 1 ( ) 1 1 ( ) 1 1 (arccos ) 1 1 (arcsin ) x arcctgx x arctgx x x x x + ′ = − + ′ = − ′ = − − ′ = ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ = + ± + ± = + = + = + ⋅ = − + ⋅ = + = = − + = = + x x a C x a dx chxdx shx C shxdx chx C C a a a dx x ctgxdx x C x tgxdx x C xdx ctgx C x dx xdx tgx C x dx x x ln( ) ln csc csc sec sec csc sin sec cos 2 2 2 2 2 2 2 2 C a x a x dx C a x a x a x a dx C x a x a x a a dx C a x arctg a x a dx xdx x ctgx C xdx x tgx C ctgxdx x C tgxdx x C = + − + − + = − + + − = − = + + = − + = + + = + = − + ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ arcsin ln 2 1 ln 2 1 1 csc ln csc sec ln sec ln sin ln cos 2 2 2 2 2 2 2 2 ∫ ∫ ∫ ∫ ∫ − = − + + − = − − + − + + = + + + + + − = = = − C a a x a x x a x dx x x a C a x a x x a dx x x a C a x a x x a dx I n n I xdx xdx n n n n arcsin 2 2 ln 2 2 ln( ) 2 2 1 sin cos 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 0 π π