Problemas resueltos de calculo integral

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• Publicado : 17 de octubre de 2010

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1) X4dx = X55+ C
I=X4+14+1 + C
I=X55 +C

2) dxx2= - 1x + C
∫x- 2 dx
I= x-2+1- 2+1+ C
I= -1X+ C

3) ∫x23 dx=3 X5/35 + C
I = x23+3323+23+ +c
I= x5353+ c
I= 3 x5/35+ c
4) ∫ dxx=2 x + c
∫ x- 1/2 dx
I= x-12+22-12+22+ c
I= x1/21/2 + c
I= 2 x1/2 + c
I= 2 x+ c
5) ∫ dx3x=3 x232+ c
∫ x2/3 dx
I= x-13+33-13+ 33+ c
I= x2323+ c
I= 3 x232+ c

6)∫ 3 a y2dy = a y3+ c
3 ∫ a y2 dy
I= 3 ay2+12+1 + c
I= 3 ay2+12+1+ c
I= 3 ay33+ c
I= ay3+ c

7) ∫ 2 dtt2= - 2t +c
∫ 2 t-2 dt
I= 2 t-2+1-2+1+ c
I= 2 t-1-1 + c
I= - 2t+ c

8) ∫ax dx = 2 x ax 3 + c
∫ ax12 dx
I= ax12+ 2/212+ 2/2 + c
I= ax3/23/2 + c
I= 2ax323+ c
I=2x22 3ax1/2 + c

9) ∫ dx2x= zx+ c
∫ 2x-1/2 dx
½ ∫ 2x-1/2 dx
I= ½ 2x-12+ 2/2-12+22 + c
I= ½ 2x1/21/2+ c
I= ½ 4x12+c
I= 4x122+ c
I= 2x12+ c
I= 2x + c

10) ∫33t dt=3t443+ c
∫3t13 dt
13 ∫t313 dt
I= 13 3t13+3313+33+ c
I= 13 3t4/34/3 + c
I= 13 9t434+ c
I= 9t4/312+ c
I= 3t4/34 + c
11) x32+2x23+ 5 x-3 dx
= 2x525- 6x535+ 10x323- 3x+c
∫ x32 dx-2 ∫x23 dx+5 ∫x12 dx-3 dx-3∫dx
I= x32+2232+22-2 x23+3323+33+5x12+2212+22-3x+c
I=x5252-2 x5353+5x3232-3x+c
I= 2x525-2 3x535+52x323-3x+c
I=2x525-6x535+10x323-3x+c

12) ∫ 4x2- 2 xx dx= 2x2-4x+c
∫ 4x2 x dx-∫2x12xdx
4 ∫ x dx-2 ∫xxdx

4∫ x dx-2∫dxx1/2

4∫ x dx-2∫x-12dx
I= 4x1+11+1-2x-12+22-12+22+c
I= 4 x22- 2 x1212+c
I= 2x2-4x12+c
I= 2x2-4x+c

13) ∫ x22-2x2dx=x36+2x+ c
∫x22dx-∫2x2dx
½ ∫x2 dx-2∫x-2 dx
I= 12x2+12+1-2x-2+1-2+1+c
I=12 x33-2 x-1-1+c
I= x36-2-1x+c
I= x36+ 2x+c

14) ∫x 3x-2dx=6x525-4x323+c
∫ x2 3x2-2dx∫3x2dx- ∫2x2dx
3∫x32dx-2∫x12dx
I= 33x5252-2x12+2212+22+c
I=3x525-2x3232+c

15) ∫x3+6x+5xdx=x33-6x+5 lnx+c
∫ x3xdx-∫6xxdx+∫5xdx
∫x2-6 ∫dx+5 ∫dxx
I= x2+12+1-6x+5x+c
I= x33-6x+5 lnx+c

16) a+bx dx=2a+bx3b32+c
∫a+bx12dx
∫a+bx12b12+22dx

I= a+bx12+22b+c
i=a+bxb3232+c
i=2a+bx3b3/2+c

17) dya-by=-2a-byb+c
∫a-by-12dy
∫a-by-12-b dy
i= a-by-12+32-b-12+22+c
a-by-b1212+c
-2 a-byb+c18.-∫a+bt2dt=a+bt33b+c
∫a+bt2bdt
i=a+bt2+1b2+1+c
i=a+bt3b3+c
i=a+bt33b+c

19) ∫x2+x22dx 2+x236+c
½ ∫2x2+x22dx
i=12 [2+x22+12+1]+c
i=12[2+x233+c
2+x263+c

20) ya-by2dy=- a-by24b2+c
∫ya-by22bdy
12∫y(a-by2bdy
i=12 a+by22b1+1+c
i=12 a+by22b2+c
i=12 a+by222b+c

i=a+by224b+c

21)∫t 2t2+3 dt = 2t2+3632+c
∫t 2t2+312dt
14∫4t2t2+312 dt
i= 14 2t2+312+2212+22+c
i= 14 2t2+3323/2+c
i= 1422t2+3332+c
i= 22t2+31232+c
i= 2t2+3632+c

22) ∫x2x+12dx=x4+4x22+c
∫x4x2+4x+1dx
∫x4x3+4x2+xdx
4∫x3dx+4∫x2dx+∫x dx
i=4x3+13+1+4x2+12+1+x1+11+1+c
i=4x44+4x33+x22+c
i=x4+4x33+x22+c
23) ∫4x2dxx3+8=8x3+83+c
∫4x2dxx3+81/2
4∫x2dxx3+81/2
43 3x2 x3+8-12dx
i=43 x3+8-12+22-12+22+c
i=43 x3+81212+c
i= 432x3+812+c
i=x3+8312+c
i=8x3+83+c
24) ∫6z dz5-3z22=15-3z2+c
6∫zdz5-3z22
-66 -6 z 5-3z2-2dxi=-5-3z2-2+1-2+1+c
i=-5-3z2-1-1+c
i= 15-3z2+c

25) ∫a-x2dx
=ax-4xax3+x22+c
∫a 2+2a-x+x2dx
∫a-2 ax+xdx
a∫dx-2a∫x dx+∫x dx
i=ax-2ax12+2212+22+x1+11+1+c
i=ax-2a x3232+x22+c
i=ax-2a2x323+x22+c
i=ax-4a x323+x22+c
i=ax-4a x x3+x22+c
i=ax-4xax3+x22+c
26) ∫a-x2dxx
-2a-x33+c
∫a-x2 x-12 dx
-2a-x2 x-12dx
i=-2a-x2+12+1+c
i=-2a-x33+c

27) ∫xa-x2dx
2ax323-x2a+2x525+c∫x12a2+2a-x+x2dx
∫x12a-2a12x12+xdx
∫ax12-2a12x+x32dx
a∫x12dx-2a ∫x dx+∫x32dx
i=ax12+2212+22-2ax1+11+1+x32+2232+22+c

i=ax3232-2ax22+x5252+c

i=2ax323-ax2+2x525+c

i=2ax323-x2a+2x525+c

28) ∫t3dta4+t4

a4+t42+c

∫t3a4+t4-12dx

14∫4t3a4+t4-12dx

i=14a4+t4-12+22-12+22+c
i=14(a4+t4)1212+c
i=142a4+t4+c
i=2a4+t44+c
i=2a4+t42+c
29) ∫dya+by3=-12ba+by2+c
∫a+by-3dy
1b∫b a+by-3dyi=1ba+by-3+1-3+1+c
i=1ba+by-2-2+c
i=1ba+by-2-2b+c
i=-12ba+by2+c

30)∫xdxa+bx23= - 14ba+bx22+c
∫x a+bx2-3dx
12b∫2bx a+bx2-3dx
i=12ba+bx2-3+1-3+1+c
i=12ba+bx2-2-2+c

i=a+bx2-2-4b+c

i=1-4ba+bx22+c

31) ∫t2dta+bt32=-13ba+bt3+c

∫t2a+bt3-2dt

13b∫3bt2a+bt3-2dt

i=13b a+bt3-2+1-2+1+c

i=a+bt3-1-3b+c

i=-13ba+bt3+c

32) ∫z a+bz32dz=a2z22+2abz55+b2z88+c
∫z(a2+2abz3+bz3)dz
∫z(...