RACIONAL

SOLUCIONES 3

SOLUCIONES

∫

1

1)

dx

=

1/3 L |x-1| - 1/6 L |x2+x+1| - 1/√3 artg [ (2x+1)/√3 ] + k

x3 -1

∫

1

2)

dx

=

1/6 L |x-3| - 1/6 L |x+3| + k

x2 - 9

∫

1

3)

dx

=

1/5 L |x+1| - 1/5 L |x+6| + k

x2+7x+6

∫

x

4)

dx

=

4/5 L |x-4| + 1/5 L |x+1| + k

x2-3x-4

∫

x2+3x-4

5)

dx

=

x + 4 L |x-4| + L |x+2| + k

x2-2x-8

∫

x2-3x-1

6)

dx

=

1/2 L|x| + L |x+1| - 1/2 L |x-2| + k

x3-x2-2x

∫

x

7)

dx

=

L |x-2| - 2 (x-2)-1 + k

(x-2)2

∫

x4

8)

dx

=

-1/2 x2 - 3x - 6 L |1-x| - 4 (1-x)-1 + 1/2 (1-x)-2 + k

(1-x)3

∫

x4-2x3+3x2-x+3

9)

dx

=

1/2 x2 + L |x| - 1/2 L |x2-2x+3| + k

x3-2x2+3x

∫

x4+8x3-x2+2x+1

10)

dx

=

L |x|-2L|x+1|-3(x+1)-1+L|x2-x+1|+2/√3 artg [ (2x-1)/√3 ]

(x2+x)(x3+1)

∫

x3+x2-5x+15

11)

dx

=

-√5 artg[ x /√5 ]+1/2 L|x2+2x+3|+5/√2 artg [ (x+1)/√2 ]

(x2+5)(x2+2x+3)

∫

x2+5x+2

12)

dx

=

L |x-1| + 3/2 artg[ (x+1) / 2 ] + k

(x-1)(x2+2x+5)

∫

3x-2

13)

dx

=

2 L |x-1| - 2 L |x| - (x-1)-1 + k

x (x-1)2

∫

4x2+x+220

14)

=

-7(x+5)-1+ L|x+5| - 1/2 L|x2-2x+10|+ artg[ (x-1) / 3 ] + k

x4+8x3+15x2+50x+250

∫

x3+x

15)

dx

=

5/16 L|x-2| + 5/16 L |x+2| + 3/16 L |x2+4| + k

x2-16

∫

x4+1

16)

dx

=

x3/3 + 5x2/2 + 19 x - 17 L |x-2| + 82 L |x-3| + k

x2-5x+6

∫

2x3+x2-5x+8

17)

dx

=

2x+4/5 L |x|+81/10 L |x2+8x+20|+181/2 artg [ (x+4)/2 ]

x3+8x2+20x

∫

x

18)

dx

=

1/4 L |x-√3| + 1/4 L|x+√3| - 1/4 L|x-1| - 1/4 L|x+1| + k

x4-4x2+3

∫

x

19)

dx

=

1/4 L|x-1| - 1/4 L|x+1| - 1/2 (x+1)-1 + k

(x-1)(x+1)2

∫

x2

20)

dx

=

x + 3 L |x2-6x+10| + 8 artg[ x-3 ] + k

x2-6x+10