Ecuaciones

1.
dxx2-1
dxx2-1=Ax-1+Bx+1
dxx2-1=Ax+1+Bx-1x-1x+1
1=Ax+1+Bx-1
si x=1→1=A1+1+B1-1→A=12
si x=-1→1=A-1+1+B-1-1→B=-12dxx2-1=12dxx-1-12dxx+1
dxx2-1=12 lnx-1-12 lnx+1+C

2.
3x2+x-2dx
3x2+x-2=Ax+2+Bx-1→3x2+x-2=Ax-1+Bx+1x+2x-1
3=Ax-1+Bx+2si x=-2→3=A-2-1+B-2+2→A=-1
si x=1→3=A1-1+B1+2→B=1
3x2+x-2dx=Ax+2+Bx-1dx
Ax+2dx+Bx-1dx=-dxx+2+dxx-13x2+x-2dx=-lnx+2+lnx-1+C

3.
1 4x2-9 dx
14x2-9=A2x+3+B2x-3
→14x2-9=A2x-3+B2x+32x+32x-3
1=A2x-3+B2x+3
1=2Ax-3A+2Bx+3B
1=x 2A-2B-3A+3B2A+2B=0 (3)
-3A+3B=1 (2)
6A+6B=0-6A+6B=2 12B=2B=16 2A+2( 16)=02A=-13A=-16
14x2-9dx=-162x+3dx +162x-3dx
=-16dx 2x+3 + 16dx2x-3

14x2-9dx=-16ln2x+3+16ln2x-3+C

4.
x+1x2+4x+3dxx+1x2+4x+3=Ax+3+Bx+1
→x+1x2+4x+3=Ax+1+Bx+3x+3x+1
x+1=Ax+1+Bx+3
x+1=Ax+A+Bx+3B
x+1=x (A+B)+A+3B
A+B=1 -3-3A-3B=-3A+3B=1 -2A =-2A=1 1+B=1B=1-1 B=0
A+3B=1x+1x2+4x+3dx=1x+3+0x+1dx

x+1x2+4x+3dx=1x+3dx +0x+1dx

x+1x2+4x+3dx=1x+3dx +0x+1dx
x+1x2+4x+3dx=Lnx+3+C