Tabla De Integrales Inmediatas 83d2h

1.

F´ ormulas de Integraci´ on Inmediata

Z 1.

dx = x + c , Z

2.

Z kdx = k

dx ,

Z 3.

Z kf (x)dx = k

f (x)dx ,

Z 4.

Z [f1 (x) + f2 (x) + ... + fn (x)] = xn dx =

Z

dx dx = ln |x| + c; x 6= 0 , x

Z

ex dx = ex + c ,

Z

ax dx =

6.

7.

8.

f1 (x)dx +

Z f2 (x)dx + ... +

xn+1 + c; n 6= −1; nQ , n+1

Z 5.

Z

ax + c; a > 0 , ln a

Z sin(x)dx = −cos(x) + c ,

9. Z 10.

cos(x)dx = sin(x) + c , Z

π sec2 (x)dx = tg(x) + c; x 6= (2n + 1) ; nZ , 2

Z

csc2 (x)dx = −ctg(x) + c; x 6= nπ; nZ ,

Z

π sec(x).tg(x)dx = sec(x) + c; x 6= (2n + 1) ; nZ , 2

11.

12.

13. Z

csc(x).ctg(x)dx = −csc(x) + c; x 6= nπ; nZ ,

14. Z 15.

π tg(x)dx = − ln |cos(x)| + c; x 6= (2n + 1) ; nZ , 2

Z ctg(x)dx = ln | sin(x)| + c; x 6= nπ ,

16. Z 17.

π sec(x)dx = ln |sec(x) + tan(x)| + c; x 6= (2n + 1) ; nZ , 2

Z 18.

csc(x)dx = ln |csc(x) − ctg(x)| + c; x 6= nπ; nZ ,

1

fn (x)dx ,

Z

x dx 1 = arctg +c , x2 + a2 a a

Z

dx 1 x−a = ln x+a + c; |x| > a; a > 0 , x2 − a2 2a

19.

20. Z 21.

a2 Z

22. Z 23. Z 24.

dx 1 x+a = ln x−a + c; |x| < a; a > 0 , 2 −x 2a

√

p dx = ln|x + x2 + a2 | + c , x2 + a2

√

p dx = ln|x + x2 − a2 | + c , x2 − a2

√

x dx = arcsen +c , a a2 − x2

Z p p xp 2 a2 25. x2 + a2 .dx = x + a2 + ln|x + x2 + a2 | + c , 2 2 Z p p xp 2 a2 26. x2 − a2 .dx = x − a2 − ln|x + x2 − a2 | + c , 2 2 Z p x xp 2 a2 27. a2 − x2 .dx = a − x2 + arcsen +c , 2 2 a

2