Sandra

xx2-7dx= u2-a2 =u=aseczdu=asec z tgz dz

xx2-72dx x=7secz
dx=7secz tgz dzx2=7sec 2 z

7secz7secz tgzdz7sec2 z-7=
49sec2 z tgz dz7sec2-1= 497sec2 z tgz dzsec2 z-1=

77sec2 z tgz dztg2 z= 77sec2z tgz dztgz=

77sec2 z dz= 77 tgz+c

Si x= 7secz =7777x2-77+c
Sec z= x7
=7777x2-7+c= x2-7+c

Parciales
5x2+3x-2x3+2x2dx
5x2+3x-2x3+2x2=5x2+3x-2x2x+2=
Ax+Bx2+Cx+2

5x2+3x-2x3+2x2=Axx+2+Bx+2+Cx2x2x+25x2+3x-2=Ax2+2x+Bx+2B+Cx2

5x2+3x-2=Ax2+2Ax+Bx+2B+Cx2

5x2+3x-2=A+cx2+2A+Bx+2B

A+C=5
2A+B=3
B=-22=-1
2A+B=3
2A+ (-1)=3
2A =3+1
2A=4
A= 42=2

A+C=5 5x2+3x-2x2(x+2)=2x+-1x2+3x+2C=5-A
C=5-2
C=3 5x2+3x-2x2(x+2)dx=2x-1x2+3x+2dx=

2dxx-dxx2+3dxx+2=
Como dvv=In v
2Inx-x-2dx+3In(x+2)
Como vndv=vn+1n+1
2Inx-x-2+1-2+1+3Inx+2+c

2Inx-x-1-1+3Inx+2+c2Inx-3Inx+2+1x+c b In a=In ab
In a +In b=In(ab)
Inx2+Inx+23+1x+c=
Inx2x+23+1x+c
x3+2x-1x3-xdx Como P(x)Q(x)dxNo cumple P(x)<Q(x)
x3+2x-1x3-x
x3+2x-1x3-x=1+3x-1x3-x
3x-1x3-x=3x-1xx2-1=3x-1xx+1(x-1)

3x-1xx+1(x-1)=AX+BX+1+Cx-1
3x-1xx+1(x-1)=AX+1X-1+Bxx+1+Cx(x+1)xx+1(x+1)3x-1=A(x2-1)+Bx2-2+C(x2+x)
3x-1=Ax2-A+Bx2-Bx+Cx2+Cx)
3x-1=(A+B+C)x2+-B+c+(-A)
A+B+C=0
-B+C=3 1+B+C=0 -B+C=3
-A=-1 B+C=-1 B+C=-1
A=12C=2
C=1
B=-C-A
B=-1-1
B=-2...