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 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. u^no du = ∫ (uⁿ⁺¹/n+1) + C, if n ≠ – 1

5. ∫ du/u = ln u + C, if u > 0

6. to^u du = a^u/lna + C, if a > 0

7. ∫ and^u du = and^u + C

8. ∫ sin u du = – cos u + C

9. ∫ cos u du = sin u + C

10. ∫ tg u du = ln sec u + C

11. ∫ cotg u du = ln sin u + C