Question $7(10$ points $)$

For ${\displaystyle \underset{0}{\overset{2}{}}}\frac{t}{\sqrt[\phantom{2}]{5+t^2}}dt,$ use a change of variables to evaluate the definite integral.

Question $8(20$ points $)$

In the following exercises, find each indefinite integral by using appropriate substitutions.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{xln(x)}$;$x>1$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{-x^2}dx$

Question $8(20$ points $)$

In the following exercises, find each indefinite integral by using appropriate substitutions.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{xln(x)}$;$x>1$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{-x^2}dx$