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

Question

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

Answer 1

The substitution u=2x²+1 along with a multiplication of the integral by 5/4 will give you an integrand of the form u^-1/2 which can be integrated by using the so-called power rule. First extract the 5 from the integrand and multiply the integral by 1/4.

I need to clarify something in my answer. The 5 comes outside the integral and the expression is multiplied by 4/4...the numerator on the inside of the integral and the denominator on the outside.