Basic Integration Formulas, Lecture notes of Mathematical Methods for Numerical Analysis and Optimization

Basic Integration Formulas lesson 1

Typology: Lecture notes

2018/2019

Uploaded on 05/14/2019

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Basic Integration Formulas
1. Zundu =un+1
n+ 1 +c, n 6=1
2. Z1
udu = ln |u|+c
3. Zeudu =eu+c
4. Zsin u du =cos u+c
5. Zcos u du = sin u+c
6. Ztan u du = ln |sec u|+c
7. Zsec u du = ln |sec u+ tan u|+c
8. Zsec2u du = tan u+c
9. Zsec utan u du = sec u+c
10. Zcot u du = ln |sin u|+c
11. Zcsc u=ln |csc u+ cot u|+c
12. Zcsc2u du =cot u+c
13. Zdu
a2u2= arcsin u
a+c
14. Zdu
uu2a2=1
aarcsec|u|
a+c
15. Zdu
a2+u2du =1
aarctan u
a+c
16. Zu dv =uv Zv du

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Basic Integration Formulas

un^ du = un+ n + 1

  • c, n 6 = − 1

u du = ln |u| + c

eu^ du = eu^ + c

sin u du = − cos u + c

cos u du = sin u + c

tan u du = ln | sec u| + c

sec u du = ln | sec u + tan u| + c

sec^2 u du = tan u + c

sec u tan u du = sec u + c

cot u du = ln | sin u| + c

csc u = − ln | csc u + cot u| + c

csc^2 u du = − cot u + c

du √ a^2 − u^2

= arcsin u a

  • c

du u

u^2 − a^2

a

arcsec |u| a

  • c

du a^2 + u^2 du =

a arctan u a

  • c

u dv = uv −

v du