Inthis problem, a sample soltrition has been witten to the given problem. However, mistakes have bejp made with those solutions.

Identify where the mistakes have been made, explain what the stucent difd wrong, and correct the solution.

a$.$

Calculate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{x^2}dx$

Solution: Since $$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{x^2}dx=ln|x^2|+C$

Because $x^2$ is always greater than or equal to $0,$ we can drop the absolute value symbols. Therefore

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{x^2}dx=ln(x^2)+C=2ln(x)+C$

Describe the mistakes. Explain your thinking fully and show your work to provide corrections to the mistakes.