Integration:Integration is the reverse process of

differentiation. Suppose ddxf ( x )=F ( x ), then F (x) is called

ant derivative or integration of the function F ( x ) with respect to x.

In symbol, we have ∫F (x )dx=f ( x )+c

Again, if ddx [F ( x )+c ] is also equal ¿F (x)

Formulae

1. ∫ kf (x )dx=k∫ f ( x )dx+c

2. ∫ [ f ( x )+g ( x ) ] dx=∫ f ( x )dx+∫ g (x )dx+c

3. ∫ xndx= xn+1

n+1+c ,n≠−1

4. ∫ dx=x+c

5. ∫ 1x dx=ln x+c

6. ∫ exdx=ex+c

7. ∫ eax dx= eax

a+c

8. ∫ (ax+b )ndx= (ax+b )n+1

a (n+1 )+c ,n≠−1

9. ∫ 1ax+b

dx=log (ax+b )

a+c

10. ∫uv dx=u∫ vdx−∫ {dudx∫ vdx}dx

11. ∫ ax dx= ax

ln a+c ,a>0

12. ∫sin axdx= cosaxa +c

13. ∫cos axdx= sinaxa +c

14. ∫sin xdx=−cos x+c

15. ∫cos xdx=sin x+c

16. ∫ cosec2 xdx=−cot x+c

17. ∫ sec2 xdx=tan x+c

18. ∫ tan xdx=log sec x+c

19. ∫ cosecx cotxdx=−cosecx+c

20. ∫cot xdx=log sin x+c

21. ∫ secx tanx dx=secx+c