Integrate 2x(x^2 + 1)^4 dx

Problem: Evaluate the indefinite integral $\int 2x(x^2 + 1)^4 \, dx$.

Steps

1. Substitute $u = x^2 + 1$
   $$\int (x^2 + 1)^4 (2x \, dx)$$
2. Substitute $du = 2x \, dx$
   $$\int u^4 \, du$$
3. Apply the power rule for integration
   $$\frac{u^5}{5} + C$$
4. Substitute back $u = x^2 + 1$
   $$\frac{(x^2 + 1)^5}{5} + C$$