integration by substitution - calc

Question

Transform this antiderivative problem using the substitution u = 5x + 1.

2x/5x + 1 dx

Your final answer should be a new antiderivative problem written in terms of the variable u.

_________________

Answer 1

2x/(5x+1)

integral = [-2(ln|5x+1| -5x)]/25

u=5x+1, du=5

-5x = 1-u

integral = [-2(ln|u| -u]/25 + c

where c = an unknown constant

2x/(5x+1)dx

=2[(u-1)/5]/u)du/5

=(2/5)(u-1)/u)du

= (-2/25)((1/u-1)

integral = (-2/25)(ln|u|-u) + c