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.

Step-by-step construction of the graph of the second degree function

Step-by-step construction of the graph of the second degree function

In Elementary School, functions are mathematical formulas that associate each number in a numeric...

read more

Mathematics in Economics: Cost Function, Revenue Function and Profit Function

An important application of Mathematics is present in Economics through the Cost, Revenue and Pr...

read more
Affine function by the value of two points. The coefficients of the affine function

Affine function by the value of two points. The coefficients of the affine function

Let's determine the function that goes through a colon. For this, we need to find the coordinate...

read more