Question

Integral indefinida de
1/x^3
X^1/3
√x
1/√x

Answer 1

Olá,

c = constante de integração

Vamos calcular as integrais indefinidas:

a)

∫ 1/x³ dx = ∫ x⁻³ dx = (x⁻³⁺¹)/(-3+1) = (x⁻²)/(-2) = -1/2x² + c

b)

∫ x^1/3 dx = x^(1/3+1)/(1/3+1) = x^(4/3)/(4/3) = 3/4 · x^(4/3) + c

c)

∫ √x dx = ∫ x^1/2 = x^(1/2+1)/(1/2+1) = x^(3/2)/(3/2) = 2/3 · x^(3/2) + c

d)

∫ 1/√x dx = ∫ 1/x^(1/2) dx = ∫ x^(-1/2) dx
∫ x^(-1/2) dx = x^(-1/2+1)/(-1/2+1) = x^(1/2)/(1/2) = 2/1 · x^(1/2) + c

∫ 1/√x dx = ∫ x^(-1/2) dx = 2√x + c

Bons estudos