TALHA SIDDIQUI’s ACADEMY OF COMMERCE & SCIENCES

021-35248855 Sir. Talha Siddiqui.

0345-3093759

INTEGRATION FORMULAE

1. vdxudxdxvu

2. dx xadx ax , where a is any constant.

3. c1n

xdxx

1nn

4.

c

1na

baxdxbax

1nn

5. cxlndx x

1

6. caln

adxa

xx

7. caln

a

n

1dxa

nxnx , where n is any constant

8. cea

1dxe axax

9.

caxax

dx

ln

10. ca

xsin

xa

dx 1

22

11. ca

xtan

a

1

xa

dx 1

22

12. ca

xsec

a

1

xax

dx 1

22

13. cax

axln

a2

1

ax

dx22

14. cxa

xaln

a2

1

xa

dx22

15. caxxlnax

dx 22

22

16. caxxlnax

dx 22

22

17. ca

xsina

2

1xax

2

1dxxa 122222

18. caxxlna2

1axx

2

1dxax 2222222

19. caxxlna2

1axx

2

1dxax 2222222

TALHA SIDDIQUI’s ACADEMY OF COMMERCE & SCIENCES

021-35248855 Sir. Talha Siddiqui.

0345-3093759

20. cxsindx xcos

21. cnx sinn

1dx nx cos

22. cxcosdx xsin

23. cnxcosn

1dx nxsin

24. cxseclndx xtan

25. cxsinlndx xcot

26. cxtanxseclndx xsec

27. cxcotecxcoslndx ecxcos

28. cxtandx xsec2

29. cxcotdx xeccos 2

30. cxsecdx tanx xsec

31. cecxcosdxcotx ecxcos

Integration By Trigonometric Substitution

An integrand which contains one of the forms 222222 ax ,xa ,xa but no other irrational

factor, may be transformed into another involving trigonometric substitution of a new variable as follows:

For use to obtain

22 xa x = a sinθ cosasin1a 2

22 xa x = a tanθ secatan1a 2

22 ax x = a sec θ tana1seca 2

Integration By Parts

Integral of product of two functions = 1st function × Integral of the 2

nd − function 1 the of Derivative st ×

Integral of 2nd

function.

dxdx vdx

dudx vudx vu