Integrate the following by using substitution rule.

Question

Integrate (5x)/(sqrt(2x ^ 2 + 1)) dx from 1 to 2 by using the substitution rule.

Answer 1

Let u = 2x²+1 du = 4xdx and substitute into integral. Since it is a definite integral we can change the bounds of 1 to 2 in x to 3 to 9 in u.

integral from 3 to 9 of 1/u^1/2 *(5/4)du (we had 5xdx and du is 4xdx - hence the 5/4)

(5/4)2u^1/2 from 3 to 9 = 15/2 - (5/2)*sqrt(3)