Q$2(10$ points$)$

Now, we are using substitution to solve questions with a linear function inside a root.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x}{(x-1{)}^{\frac{1}{2}}}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x\sqrt[3]{x-1}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x(x-2{)}^{\frac{1}{2}}+\frac{x}{(2x+1{)}^{\frac{3}{2}}}dx$ Hint: Split this into two integrals and use a different substitution for each part.