Maths problem (integration)

Gradient of a curve is given by:

dy/dx= 2x/x^2+e

The curve passes through the point (0,2)

What is the equation of the curve?

∫ 2x/(x^2 + e) dx

Let u = x^2 + e
then du = 2x dx

y = ∫ 1/u du

y = ln u + c
y = ln (x^2 + e) + c

Using the point (0,2),

2 = ln (0 + e) + c
2 = 1 + c
c = 1

y = ln(x^2 + e) + 1