x xx2 Ł ł ax x a dx = ln a + C x = ( )ó 2 1x xdx = - x + C sin cos
ax = ax a ( )ó ln xdx = x + C cos sin
1 x = log ( )ó x ln a a tgxdx = -ln cos x + C x =1 ln ( )ó x ctgxdx = ln sin x + C dx x = x (sin )ó cos = tgx + C
x =- xcos2 x cos ( )ó sin 1 dx tgx = = -ctgx + C ( )ó cos2 x
sin2 x 1 dx 1 x ctgx =- = arctg + C ( )ó sin2 x
x2 + a2 aa 1 dx 1 x - a arcsin x = ( )ó =+ C ln
1- x2 x2 - a2 2a x + a 1 dx x arccos x =- =arcsin + C ( )ó
a 1- x2 a2 - x2 dx arctgx = ( )ó x21+1 = x + x2 + q + C ln
x2 + q arcctgx =- ( )ó x21+1 cos2x=cos^2x-sin^2x a[(x+b/2a)^2-d/4a^2] ó b ł óó f x f x g x - f x g x ( ) ( ) ( ) ( ) ( ) = ę 2 łł g x ł ( )ś g x ł P = +"łg (x) - f (x)ł dx ( )
a o 45o 90o 60o 30 b 2 o p p p p Ą = ( ) V +" f x dx 0 ab 6 3 4 2 0 2 V g2 x f x d x ( ) ( )ł +"ł - łł =Ą ł 1 2 a 3 0 1 arc sin x ( ) b 2 2 2 2 2 L = 1+ ł f x łł dx ( )ł +" ł 3 2 1 a b 1 arc cos x ( ) 0 2 2 Pp =2Ą f x 1+ł f x łł dx 2 ( ) ( )ł 2 2 +" ł a 3 arc tgx 0 ( ) 1 Ą 3 3 3 arc ctgx Ą ( ) 3 1 0 3