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DEPARTAMENTO DE PREPARATORIA AGRICOLA

AREA DE MATEMATICAS
CALCULO INTEGRAL
PRESENTA:
VASQUEZ JIMENEZ ROSY MAYRA

GRADO:GRUPO:
materia | CALCULO INTEGRAL |

3º “2”

1) x2-2x-1x+2dx=x2-2x-1x+2=x-4+7x+2=x-4dx+71x+2dx = udu+7du1u1 = u22+7lnx+2+c=(x-4)22+7ln(x+2)+c
u=x-4 u1=x-2
du=dx du1=dx
2) 5X+5Xdx=5xdx+5x dx= u1/2du+51xdx =2u323+5 duu112=25x33+5u1-12du=25x33+5(2u112)+c= 25x33+25 x+c= 25x33+ 25x+c=

u=5x u1=x
du=dx du1=dx

3) 1+x1-xdx=1+x1-x1+x1+xdx= 1+x1-x2dx=dx1-x2+x1-x2dx= dua2-x2-12duu12
Arcsenx-12u1212+c=Arcsenx-1-x2+c
u=1-x2
-du2=xdx u=x a=x

4) 2x+59-x2 dx=2x9-x2 dx+5dx9-x2=2-2duu12+5dua2-u2 =-29-x2 +5arcsenx3+c
u=9-x2
- du2=x u=x a=3

5) sec3xtanxdx= sec2xsecxtanxdx=udu=u33+c=sec3x3+c
u=secx
du=secxtanxdx

6)senϕ+tanϕcosϕdx=tanϕ+tanϕcosϕ=lnsecϕ+senϕcosϕcosϕdϕ=Insecϕ+senϕcos2ϕdϕ=Insecϕ-du u2=Insecϕ-u-1-1= Insecϕ+1cosϕ+c = Insecϕ+secϕ+c
u=cosϕ
-du=senϕdϕ

7) dxe2x+3=1e2x+3=13-e2x3(e2x+3)=13dx-13e2xe2x+3 =13x-13*12duu=13x-16lne2x+3+cu=e2x+3
du2=e2xdx

8) tt+3dt=12(u2-3 u)udu =12u33-32u+c= 16t+3 3-32t+3 +c
u=t+3 u2=t+3 t=u2-3 dt2=udu

1) dxx2+4x+3=dxx2+4x+3+1-1=dxx+22-1=duu2-a2=12alnu-au+a+c=12(1)lnx+2-1x+2+1+c=
12lnx+1x+3+c

u2=x+22 ; a2=1
u=x+2 ; a=1
du=dx

2) dx2x-x2-10=dx-x2-2x+10=dx-x2-2x+1+9=-dx(x-1)2+9
=-duu2+a2=-1aarctanua+c=-13arctanx-13+c
=-13arctanx-13+cu2=(x-1)2 ; a2=9
u=x-1 ; a=3
du=dx

3) dxx2-8x+25=dxx2-8x+16+9=dx(x-4)2+9
=duu2+a2=1aarctanua+c
=13arctanx-43+c
u2=x-42 ; a2=9
u=x-4 ; a=3
du=dx

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