Fundamental Integration Formulas

Integrate means to determine the primitive function in relation to a previously derived function, that is, we will perform an inverse operation of the derivation. We call a function F(x) of primitive f(x) at a given interval, only if for all I we have F’(x) = f(x).
If F(x) is an integral of f(x), then F(x) + C is also, C being an arbitrary constant. For example, the functions given by x², x² + 6, x² - 2 and x² + 10 are integrals of 2x, given that d/dx (x²) = d/dx (x² + 6) = d/dx (x² - 2) = d/dx (x² + 10) = 2x.

To perform the function integrations, aiming to discover the primitive function, we use some fundamental integration formulas. Watch:

1. ∫ d/dx [f (x)] dx = f (x) + C

2. ∫(u + v) dx = ∫ u dx + ∫ v dx

3. ∫ au dx = a ∫ u dx, where a is any constant.

4. uno du = ∫ (un+1/n+1) + C, if n ≠ – 1

5. ∫ du/u = ln u + C, if u > 0

6. tou du = au/lna + C, if a > 0

7. ∫ andu du = andu + C

8. ∫ sin u du = – cos u + C

Do not stop now... There's more after the advertising ;)

9. ∫ cos u du = sin u + C

10. ∫ tg u du = ln sec u + C

11. ∫ cotg u du = ln sin u + C

12. ∫ sec u du = ln (sec u + yg u) + C

13. ∫ cosec u du = ln (cosec u – cotg u) + C

14. ∫ sec² u du = tg u + C

15. ∫ cosec² u du = – cotg u + c

16. ∫ sec u tg u du = sec u + C

17. ∫ cosec u cotg u du = – cosec u + C

18.

19.


20.


21.


22.


23.


24.


25.

26.

by Mark Noah
Graduated in Mathematics
Brazil School Team

Occupation - Math - Brazil School

Would you like to reference this text in a school or academic work? Look:

SILVA, Marcos Noé Pedro da. "Fundamental Integration Formulas"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/formulas-fundamentais-integracao.htm. Accessed on June 29, 2021.

Inverse function: what is it, graph, exercises

Inverse function: what is it, graph, exercises

THE inverse function, as the name suggests, is the function f(x)-1, which does exactly the invers...

read more
Composition of three or more roles

Composition of three or more roles

Work with composite functions it doesn't have big secrets, but it requires a lot of attention and...

read more
Logarithmic Function. Study of the Logarithmic Function

Logarithmic Function. Study of the Logarithmic Function

Every function defined by the formation law f (x) = logThex, with a ≠ 1 and a > 0 is called th...

read more