How do you evaluate the integral of 2udu divided by 1 plus u squared?

Answer 1

for the integral of (2x)dx/(1+x2 )

Take (1+x2 ) as your 'u' substitution.

find du, du= 2x dx

use u substitution to write new integral, integral of du/u

the integral of du/u= ln abs(u) + C

therefore, your original problem becomes an answer with ln

ln abs (1+x2) + C

*abs refers to absolute value of the parentheses