Integral of \( \displaystyle 2 x + \frac{1}{2 x} \)

Problem 4.275 · medium

1. \[ \int \left(2 x + \frac{1}{2 x}\right)\, dx \]
   integralStart with the integral of the given expression.✓ Proved
2. \[ = \int \frac{1}{2 x}\, dx + \int 2 x\, dx \]
   linearity algebraSplit the integral into two parts using linearity. Factor out the constant 1/2 from the second term.✓ Proved
3. \[ = \frac{\int \frac{1}{x}\, dx}{2} + 2 \int x\, dx \]
   algebraFactor out the constant 2 from the first term.✓ Proved
4. \[ = x^{2} + \frac{\ln{\left(x \right)}}{2} \]
   antiderivativeEvaluate the integrals of x and 1/x.✓ Proved