Evaluate 2x(1-x^3)dx

Answer 1

To evaluate this integral, we need to distribute the 2x into the expression 2x(1-x^3):

2x(1-x^3)dx
= 2x - 2x^4 dx
= 2x dx - 2x^4 dx

Now we can integrate each term separately:

∫2x dx = x^2 + C1
∫-2x^4 dx = -1/2 * x^5 + C2

Therefore the final result is:

x^2 - 1/2 * x^5 + C