Integrales inmediatas por cambio de variable

 Antes de pasar a estudiar la integral definida, vamos a repasar integrales inmediatas por cambio de variable:

1. ∫u'·u^m dx = u^m+1/m+1 + C, si m ≠ -1
2. ∫(u'/u)dx = Ln|u| + C
3. ∫(u'·a^u)dx = a^u/Ln a + C, a > 0 y a ≠ 1
4. ∫(u'·e^u)dx = e^u + C
5. ∫(u'·sen u)dx = -cos u + C
6. ∫(u'·cos u)dx = sen u + C
7. ∫(u'·tg u) dx = -Ln|cos u| + C
8. ∫(u'·cotg u)dx = Ln|sen u| + C
9. ∫(u'/cos² u)dx = ∫u'·sec²u dx = tg u + C
10. ∫(u'/sen² u)dx = ∫(u'·cosec²u) dx = -cotg u + C
11. ∫u'·sec u·tg u dx = sec u + C
12. ∫u'·cosec u ·cotg u dx = -cosec u + C
13. ∫[u'/√(1 - u²)]dx = arc sen u + C = -arc cos u + C
14. ∫[u'/(1+u²)]dx = arc tg u + C = -arc cotg u + C
15. ∫[u'/u√(u²-1)]dx = arc sec u + C = - arc cosec u + C
16. ∫[u'/√(u²+1)]dx = Ln|u + √(u² + 1) + C
17. ∫[u'/√(u² - 1)]dx = Ln|u + √(u²-1)| + C
18. ∫[u'/(u²-1)]dx = (1/2)·Ln|(u-1)/(u+1)| + C
19. ∫[u'/(1-u²)]dx = (1/2)·Ln|(1+u)/(1-u)| + C