工程数学常用之微积分公式

1.

1)(−=n n nx x dx d 2.

ax ax ae e dx d =)( 3.

0,1)(ln >=x x x dx d 4.

x a ax dx d cos sin = 5.

x a ax dx d sin cos −= 6.

x x dx d cosh sinh = 7.

x x dx d sinh cosh = 8.

)(')]([x cf x cf dx d = 9. )(')(')()()]()([x g x f x g dx

d x f dx d x g x f dx d +=±=± 10. product rul

e ：

)(')()()(')]()(x g x f x g x f x g x f dx d +=⋅ 11. quotient rule ：2)]

([)(')()()(')()(x g x g x f x g x f x g x f dx d −=⎥⎦⎤⎢⎣⎡ 12. the chain rule ：

)('))(('))((x g x g f dx dg dg df x g f dx d =⋅=

1. ⎪⎩⎪⎨⎧−≠++−=+=+∫1for ,11for ,ln 1n c n x n c x dx x n n

2. c e a dx e ax ax +=∫1

3. c ax a axdx +−=∫cos 1sin

4. c ax a axdx +=∫sin 1cos

5. ]cos sin [sin 22bx b bx a b a e bxdx e ax ax −+=∫

6. ]sin cos [cos 22bx b bx a b a e bxdx e ax ax ++=∫

7. ∫∫=dx x f c dx x cf )()]([

8. ∫∫∫±=±dx x g dx x f dx x g x f )()()]()([

9. )(')]([x cf x cf dx d = 10. ∫∫−⋅=vdu v u udv