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Cálculo Integrales Inmediatas y Derivadas
Contributed by: Ortiz Corredor
  • 1. Calcular ∫(x3 + 4·x2)dx
A) x3/4 - 4·x3/3
B) x4/4 + 4·x3/3
C) x4/4 - 4·x3
D) 4x4/4 - 4·x3/3
  • 2. Calcular ∫((4+x2)/x2)dx
A) 4x - 1/x
B) -x + 4/x
C) -2x - 4/x
D) x - 4/x
  • 3. Calcular ∫(4x1/2+2x2/3)dx
A) -6·x5/3/5 + 8·x1/2/3
B) 6·x5/3/5 -8·x3/2
C) 6·x5/3/5 + 8·x3/2/3
D) x5/3/5 - 8·x3/2/3
  • 4. Calcular ∫((1+x2)2)dx
A) -(3·x4 + 10·x2 + 15)/15
B) x·(3·x4 + 10·x+ 15)/15
C) x·(3·x4 + 10·x2 - 15)
D) x·(3·x4 + 10·x2 + 15)/15
  • 5. Calcular ∫((2+3/x3))dx
A) -x - 3/(2·x2)
B) 2·x - 3/(2·x2)
C) -2·x + 3/(2·x2)
D) 2·x +1/(2·x)
  • 6. Calcular ∫(x3(x5-1/2x2))dx
A) x9 + x6/12
B) -9x9 - x6/12
C) -x9/9 +5 x6/12
D) x9/9 - x6/12
  • 7. Calcular ∫((√x-x7)/√x)dx
A) x - 2·x15/2/15
B) x + 2·x15/2
C) -x - 2·x1/2/15
D) x - 4x15/2/15
  • 8. Calcular la derivada de f(x)=(x-√x)/cosx
A) (1 - 1/(2·√x))/COS(x) + √x·(√x - 1)·SIN(x)/COS(x)2
B) (1 + 1/(2·√x))/COS(x) - √x·(√x - 1)·SIN(x)/COS(x)2
C) (1 - 1/(2·√x))/COS(x) + √x·(√x - 1)·SIN(x)/COS(x)
D) (1 - 1/(2·√x))/COS(x) + √x·(√x - 1)·COS(x)/SIN(x)2
  • 9. Calcular la derivada de f(x)=(x2a2)/(x3+a3)
A) a2·x·(2·a3 - x3)/(x3 + a3)2
B) a2·x·(2·a3 - x3)/(x3 + a3)
C) a·x·(2·a3 - x3)/(x3 - a3)2
D) -a2·x·(2·a3 - x3)/(x3 - a3)2
  • 10. Calcular la derivada de f(x)=(x2+x+1)/(x2-x+1)
A) (1 - x2)/(x2 - x + 1)
B) 2·(1 - x2)/(x2 - x + 1)2
C) 2·(1 - x2)/(x2 - x + 1)
D) -2·(1 - x2)/(x2 + x + 1)2
  • 11. Calcular la derivada de f(x)=(x2+x+1)2
A) -2·(x2 + x + 1)·(2·x + 1)
B) -2·(x2 - x - 1)·(2·x + 1)
C) 2·(x2 + x + 1)·(x - 1)
D) 2·(x2 + x + 1)·(2·x + 1)
  • 12. Calcular la derivada de f(x)=√(x2+x)
A) (2·x + 1)/(2·√((x + 1)))
B) (2·x + 1)/(2·(x·(x + 1)))
C) (2·x + 1)/(2·√(x·(x + 1)))
D) -(x + 1)/(2·√(x·(x - 1)))
  • 13. Calcular la derivada de f(x)=√(1+x+x2)
A) -(2·x + 1)/(2·√(x3 + x + 1))
B) -(2·x + 1)/(2·√(x2 - x - 1))
C) (2·x + 1)/(2·√(x2 + x + 1))
D) (2·x + 1)/(2(x2 + x + 1))
  • 14. Calcular la derivada de f(x)=1/√(x+1)
A) 1/(2·(x - 1)3/2)
B) - 1/(2·(x + 1)3/2)
C) - 1/(2·(x - 1)5/2)
D) 1/(2·(x + 1)1/2)
  • 15. Calcular la derivada de f(x)=x/(√(x2+1))
A) -1/(x3 + 1)3/2
B) -1/(x2 + 1)1/2
C) 1/(x2 - 1)1/2
D) 1/(x2 + 1)3/2
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