高等數学复习公式 高等数学公式 导数公式 (gx)=sec x (arcsin x) (csc x)=-cScxctgx (a)=a In (log x)= In a (arcctgx= 1+x 基本积分表: tgrdx=-In/cos x +C dx In/sin x +C csc xdx=-ctgx+C sec xdx= hn secx+tgx+C sin x csc xdx= In/csc x-ctgx+C sec x.tgxdx= sec x+C dx C In 2 shxdx=chx+C In x22 I chxdx= shx+C arcsin - n-1 x +a dx +a2+mn(x+√x2+a2)+C dh x arcsin -+C 三角函数的有理式积分: 2 sInx= cOSx= =tg 2a。2h 1+u 第1页共15页高等数学复习公式 第 1 页 共 15 页 高等数学公式 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 t g 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