Cálculo Antiderivadas Básicas y Sustitución
  • 1. Calcular: ∫(1/x + x3)dx
A) LN(x) + x4 + c
B) 4LN(x) + x4/4 + c
C) 4LN(x) + x4 + c
D) LN(x) + x4/4 + c
  • 2. Calcular: ∫(sec2x-secx*tanx)dx
A) - LN(SIN(x) + 1) + c
B) - COT((2·x + π)/4) - x + c
C) tanx+secx +c
D) tanx-secx +c
  • 3. Calcular ∫(4ex)dx
A) 4·ex + c
B) lnx + 4 + c
C) ex/4 + c
D) ex + c
  • 4. Calcular ∫(-senx)dx
A) -sen(x)*COS(x) + c
B) COS(x) + c
C) -COS(x) + c
D) -sen(x) + c
  • 5. Calcular ∫(3x+4x)dx
A) 3x/LN(3) + 42·x - 1/LN(2) + c
B) 3x/LN(3) + 2x - 1/LN(2) + c
C) 3x/LN(3) + 22·x + 1/LN(2) + c
D) 3x/LN(3) + 4x/LN(4) + c
  • 6. Calcular ∫(x2lnx)dx
A) x3/(3x)(ln3x-1/(3x))+C
B) x9/3(lnx-1/9)+C
C) x3/3(lnx-1/3)+C
D) x2/2(lnx-1/2)+C
  • 7. Calcular ∫(xcosx)dx
A) cosxsinx+x+C
B) x2sinx+cosx2+C
C) xcosx+sinx+C
D) xsinx+cosx+C
  • 8. Calcular ∫(xex)dx
A) 2xe-x-ex+C
B) xe2x-ex +C
C) ex(x-1)+C
D) ex(x+1)+C
  • 9. Calcular ∫sin(lnx)dx
A) 1/2[x(cos(lnx)-sin(lnx))]+C
B) 1/2[x(ln(cosx)-ln(sinx))]+C
C) 1/2[x(sin(lnx)-cos(lnx))]+C
D) 1/2[x(ln(sinx)-ln(cosx))]+C
  • 10. Calcular ∫x3cosxdx
A) (x3-6x)sinx+3(x2-2)cosx+C
B) (x3+6x)sinx-3(x2+2)cosx+C
C) (x6-3x)cosx+6(x4-4)sinx+C
D) (x6+3x)cosx-6(x4+4)sinx+C
  • 11. Calcular ∫dx/(x2+x-6)
A) Ln((x+2)(x-3)1/5)+C
B) Ln((x+3)/(x-2)1/5)+C
C) Ln((x-2)(x+3)1/5)+C
D) Ln((x-2)/(x+3)1/5)+C
  • 12. Calcular ∫(5x+3/(x2+2x-3)dx
A) Ln((x-3)2(x+1)3)+C
B) Ln((x-3)3(x+1)2)+C
C) Ln((x+3)3(x-1)2)+C
D) Ln((x+3)2(x-1)3)+C
  • 13. Calcular ∫(x+2)sin(x2+4x-6)dx
A) 1/2csc(x2+4x-6)+C
B) 1/2tan(x2+4x-6)+C
C) 1/2sin(x2+4x-6)+C
D) -1/2cos(x2+4x-6)+C
  • 14. Calcular ∫xcot(x2+1)dx
A) 1/2cos(ln(x2+1)+C
B) 1/2sin(ln(x2+1)+C
C) 1/2ln(sin(x2+1)+C
D) 1/2ln(cos(x2+1)+C
  • 15. Calcular ∫(1+y4)1/2y3dy
A) 1/3(1-y4)3/2+C
B) 1/6(1-y4)2/3+C
C) 1/3(1+y4)2/3+C
D) 1/6(1+y4)3/2+C
  • 16. Calcular ∫(Atan(w/2))/(4+w2)dw
A) 1/4(Atan(w/2))2+C
B) 1/2(Asin(w/2))2+C
C) 1/8(Atan(w/4))5+C
D) 1/4(ASec(w/2))3+C
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