taller de integrales

MARIA MONICA SALGADO MOLINA
TRABAJO DE CÁLCULO
34.
dx5+4secxdx5+41cosx =dx51+4cosxdx5cosx+4 cosx =dx5+4cosx2dz1+z25+411-z21+z2=2dz1+z25+4(1+z2)1-z2 =2dz1+z25(1-z2)1+z226377551104014456616617997a=3 z2=3 sen θz2=9 sen2 θ dz=3cos θdθ00a=3 z2=3 sen θz2=9 sen2 θ dz=3cos θdθ=2dz1+z25-5z2+4+4z21-z2=2dz1+z29-z21+z2 =2dz9-z2 23cosθ dθ9-9sen2θ =23cosθdθ9(1-sen2θ) =69 =23 =cosθdθcos2θ23cosθdθ =231dθcosθ=23secθdθz=3senθ z3senθ23senθ23sensen-123+c86.
01x31+x2dxx∙x21+x2dxv=1+x2 → x2=v-1dv=2xdx dv2=xdx12(u-1)u du12u∙u12du-u12du12u32du12u12du=12∙25u52-12∙23u32+c=15u52-13u32+c=151+x252-131+x232+cx31+x2dx=(1+x2) 55 - (1+x2 ) 33+c01x31+x2dx =011+x2) 55-(1+x2) 33=1+1)55-(1+x)33-15-13=2215+215=2+2215=0,321972.021-xdxx2+3x+21-xdx(x+2)(x+1)1-x(x+2)(x+1)=Ax+2+Bx+1=Ax+A+Bx+2B=xA+B+A+2BA+B=-1→Ec 1
A+2B=1 →Ec 2DESPEJAMOSEc 1
Remplazamos el valor de A en Ec 2
A=-1-B-1-B+2B=1B-1=1 B=2Remplazamos B=2 En Ec 1
A+2=-1A=-3-3X+2dx+2x+1dx-3x+2dx v=x+2dv=dx-3udu=-3lnu+c=-3lnx+2+c2x+1dx v=x+1 dv=dx2udu=2ln u+c=2lnx+1+c1-xx2+3x+2=-3lnx+2+2lnx+1+c021-xx2+3x+2dx=023lnx+2+2ln(x+1)=-3ln2+2+2ln(2+1)--3ln2+2ln(1)=0,11778MARTHA CECILIA VERGARA FLORES37. sen x1+ cos2x dx sea u=cosx= -du1+ u2 du=-sen x dx=-tan-1u+c- du=sen x dx=-tan-1(cosx)+c
75. aa2(a2-x2)3 x2dxsea
x=a sen θ
dx=acosθ dθ
a2-x2=a2-a2sen2θ
=a2(1-sen2θ)
=a2cos2θx2=a2sen2θ
aa2(a2-x2)3 x2dx
=aa2(a2cos2θ)3∙ acosθ dθa2sen2θdx
128206524447594996041910= aa2a3cos3θ ∙a cosθ dθa2sen2θ
=aa2a2cos4θ sen2θ dθ
=a2aa2(cos2θ)2 sen2θ dθ...