Evaluation by substitution
Definite integration · Mathematics
Study notes
Q: Evaluate the integral from 0 to 1 of 2x(x^2+1)^3 dx. Let u = x^2+1. When x=0, u=1; when x=1, u=2. du = 2x dx. Integral becomes: integral from 1 to 2 of u^3 du = [u^4/4] from 1 to 2 = 16/4 - 1/4 = 15/4.