(7) (8)(2x+3)dx,(9) arcsin√1-x (10) dx,(11) (12) (1+x2) 解:(1) d(sin x) C 6 2)∫cos3xdx= )d(sin x) +c (3)J(x+ x-2cos√x+C ∫xe'dx= Jed(x)=ex+c (5 ∫(1-x2)2d(1 C I d x2+c xdr=[ n2 ∫h2xd(h2x)=h2x+ d(arcsin x)=h arcsin x +C arcsin x d(arctan x)=In arctan x +C (+x)arctan x arctan x(4) xe x x d 2 , (5) − 2 1 d x x x , (6) − 4 1 d x x x , (7) x x x d ln 2 , (8) (2x 3) dx 2 + , (9) − dx x x 2 1 1 arcsin 1 , (10) + x x x d (1 ) arctan 1 2 , (11) + 2 2 d x x , (12) − 2 4 d x x . 解:(1) C x x x = + 6 sin sin d(sin ) 6 5 . (2) cos x dx (1 sin x)cos x dx 3 2 = − = (1 sin )d(sin ) 2 − x x = d(sin ) sin d(sin ) 2 x − x x = C x x − + 3 sin sin 3 . (3) x x x x x x x x )d d 2 sin d sin ( + = + = x C x − 2cos + 2 2 . (4) x x x C x x x = = + 2 2 2 e 2 1 e d( ) 2 1 e d 2 . (5) x x x x C x x = − − − = − − + − − 2 2 2 1 2 2 (1 ) d(1 ) 1 2 1 d 1 . (6) x C x x x x x = + − = − 2 2 2 2 4 arcsin 2 1 1 ( ) d( ) 2 1 1 d . (7) x x x x C x x x x x = = = + ln 2 2 1 d(2 ) ln 2 d(ln 2 ) 2 ln 2 d ln 2 2 . (8) x + x = x + x + = x + + C 2 2 3 (2 3) 6 1 (2 3) d(2 3) 2 1 (2 3) d . (9) x x C x x x x = = + − d(arcsin ) ln | arcsin | arcsin 1 d 1 1 arcsin 1 2 . (10) x x C x x x x = = + + d(arctan ) ln | arctan | arctan 1 d (1 ) arctan 1 2