You are almost right you misused the natural log,Originally Posted byalysha27

Given,

use the substitution then by the substitution rule we have,

Now consider this integral as,

. Use integration by parts to get,

.

Notice this new integral is solvable by substitution, call , thus,

.

Thus, by the exponent rule,

substitute back,

substiute back,

Remember to mutiply by 1/2 as in the beginning of problem,

Q.E.D.