Integrales - Apunts 6 PDF

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Summary

Tablas integración...

Description

Integrals indefinides

a)

Z

x dx

b)

Z

1 dx x

c)

Z

d)

Z

e)

Z

sin x dx

=

f)

Z

cos x dx

=

g)

Z

1 dx cos2 x

h)

Z

1 dx 1 + x2

j)

Z

1 √ dx 1 − x2

n

x

e dx x

a dx

= =

C` alcul

xn+1 si n6= −1 n+1

Z

[f (x))]n f ′ (x) dx

=

b’)

Z

f ′ (x) dx f (x)

=

  ln |f (x)|

c’)

Z

ef (x) f ′ (x) dx

=

ef (x)

d’)

Z

af (x) f ′ (x) dx

=

af (x) ln a

− cos x

e’)

Z

f ′ (x) sin[f (x)] dx

=

− cos[f (x)]

sin x

f’)

Z

f ′ (x) cos[f (x)] dx

=

sin[f (x)]

g’)

Z

f ′ (x) dx cos2 [f (x)]

=

tan[f (x)]

h’)

Z

f ′ (x) dx 1 + (f (x)2 )

=

arctan[f (x)]

j’)

Z

=

arcsin[f (x)]

ln |x| x

e

=

ax ln a

=

=

[f (x))]n+1 si n 6= −1 n+1

a’)

=

=

EEBE

tan x

arctan x

arcsin x

f ′ (x) p

1 − (f (x)2 )

dx

Calculeu les seg¨ uents integrals Z 3 x 4 1. (x2 − + dx) = x 4 1 Z ln x dx = 2. x Z 3. cos x sin5 x dx = 4.

Z

3x sin 2x dx =

5.

Z

cos2 x dx =

6.

Z

5x2 dx = 1 + x6

7.

Z

8.

Z

sin(4x − 2) dx

15.

Z

5x cos x2 dx

16.

Z

√

17.

Z

5(x − 2x3 ) dx = (x2 − x4 )3

18.

Z

sin x cos5 x dx = π

19.

Z Z

π

Z

π

Z

π

6x2 + 2x 1 − x2 − 2x3

dx =

sin 2x cos 5x dx =

−π

(x2 + 5x) dx = 20. x +5 dx = x

9. 10.

Z

2x + 3 dx = 2 x + 3x − 5

11.

Z

sin2 x cos x dx =

12.

Z

2x dx 1 + x4

Z

ln x dx x

sin 3x cos 3x dx =

−π

2

Z

13.

14.

Z

21.

sin 4x sin 4x dx =

−π

ex sin ex dx = 22.

cos x cos 3x dx =

−π

23. dedu¨ıu en general Z π cos nx cos mx dx = −π π

Z

−π Z π −π

cos nx sin mx dx = sin nx sin mx dx =...