c o s s i n (s i n c o s )(c o s

s i n s i n y x x x x x d y x x x x x x d x '=++-+⇒=+-+ 6．设函数()y y x =由方程33ln()cos x y x y x +=+确定，求

d y

d x 332231ln()cos (3)3sin cos x y x y x x y x y x y x x y

''+=+⇒+=-++ 352322

1()cos 33sin sin 3d y x x y x y x x y x

y x x y d x +---'∴==-+ 计算下列积分：

1．

00000111sin 3cos3cos3cos3333111sin 3393x x d x xd x x x xd x

x π

ππππππ=-=-+=+=⎰⎰⎰ 2．

()d ln ln(12ln )12ln 12l 12n x d x x C x x x ==++++⎰⎰

3．

2222e d 222x x x x x x x x x x de x e e xd x x e xe e C -------=-=-+=---+⎰⎰⎰

4． 23d 65x x x x +-+⎰ 23(5)(1)3126515

x A B A x B x x A B x x x x +=+⇒-+-=+⇒=-=-+-- 22312(5)d ln 65151x x x d x C x x x x x +--⎛⎫∴=+=+ ⎪-+---⎝⎭

⎰⎰ 5．

()222222222121111d arctan (1)11x x x x d x d x x C x x x x x x x +++⎛⎫==-=-++ ⎪+++⎝⎭

⎰⎰⎰ 6.

211111ln 2(2)2222d x x d x d x C x x x x x x x ⎛⎫==-=+ ⎪++++⎝⎭⎰

⎰⎰ 7． 1ln e 1211001ln 13d (1ln )ln (1)22x u e x x x d x u du u u x =+⎛⎫=+=+=+= ⎪⎝⎭⎰⎰⎰ 8．