Question

How do you do this question?

Answer 1

Step-by-step explanation:

∫ erf(x) dx

Integrate by parts.

If u = erf(x), then du = 2/√π e^(-x²) dx.

If dv = dx, then v = x.

∫ u dv = uv − ∫ v du

= x erf(x) − ∫ 2/√π x e^(-x²) dx

= x erf(x) + 1/√π ∫ -2x e^(-x²) dx

Substitution.

If u = -x², then du = -2x dx.

= x erf(x) + 1/√π ∫ e^u du

= x erf(x) + 1/√π e^u + C

= x erf(x) + 1/√π e^(-x²) + C