integration Formulas

INTEGRATION
List of formulae

1. = 2. = ex + c
3. = kx + c 3. = log x + c
5. sin x dx = – cos x + c 6. cos x dx = sin x + c
7. sec2x dx = tan x + c 8. cosec2 x dx = – cot x + c
9. sec x tan x dx = sec x + c 10. cosec x cot x dx = – cosec x + c
11. = sin-1x + c 12. = tan-1x + c
13. = sec–1x + c 14. tan x dx = log (sec x) + c
15. cot x dx = log(sin x) + c 16. sec x dx = log(sec x + tan x) + c
17. cosec x dx = – log (cosec x + cot x) + c 18. logx dx = x logx – x + c
19. + c 20. = tan–1 + c
21. = log +c 22. = log + c
23. = log + c 24. = log + c
25. dx = + + c
26. dx = - log + c
27. dx = + log + c
28. Integration by parts

If we take f(x) as the first function and g(x) as the second function, using the order of ‘ILATE’ then
= f(x) -

Remark 1.

To integrate the second and third powers of sine and cosine of angles use the following formulae

1. Sin2 x = 2. cos2 x =
3. sin3x = 4. cos3 x =


Remark 2

To integrate the products of sine and cosine of angles use the following formulae

1. sin A cos B = [sin(A+B) + sin (A–B)]
2. cos A sin B = [sin(A+B) – sin (A–B)]
3. cos A cos B = [cos(A+B) + cos (A–B)]
4. sin A sin B = [cos(A–B) – cos (A+B)]
= = = 2 tan-1x


Types of Integrals

1. = logf(x) + c 2. =2 + c
3. [f(x)]n f’(x) dx = +c

Integration of type and

Since sin x = and cos x =
Take t = tan (x/2) Þ sin x= and x = 2 tan-1t
Þ dx = and then substitute in the given integral

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