Question

(b)∫1/√x+1-√x dx
(d)∫√x/1+x√x dx
(f)∫xᵉ⁻¹+eˣ⁻¹/xᵉ+eˣ dx
(h)∫x²+x/2x+1 dx

Answer 1

repuesta

(b) ∫(1/√(x+1) - √x) dx = 2√(x+1) - (2/3)x^(3/2) + C

(d) ∫(√x / (1 + x√x)) dx = 2arctan(√x) + C

(f) ∫(xᵉ⁻¹ + eˣ⁻¹) / (xᵉ + eˣ) dx = ln(|xᵉ + eˣ|) + C

(h) ∫(x² + x) / (2x + 1) dx = (x^2/2) + (3/4)x - (1/2)ln|2x + 1| + C

Donde C es la constante de integración.