Compute ${\displaystyle \underset{4}{\overset{13}{}}}\frac{x^2}{x-3}dx.$

Use the $u-$substitution method with $u=x-3$

In this case:

$du=,dx$

$,=x^2,($ write function $ofu)$

$,=\frac{x^2}{x-3},($ write function $ofu)$

Therefore:

${\displaystyle \underset{4}{\overset{13}{}}}\frac{x^2}{x-3}dx={\displaystyle \underset{L}{\overset{U}{}}}f(u)du$

$={\displaystyle \underset{L}{\overset{U}{}}}$

with $L=,$ and $U=$

What is the anti$-$derivative $($in terms of variable $u)$ of the integrand above?

anti$-$derivative of $f(u)=,+C$

What is the EXACT numerical value of ${\displaystyle \underset{4}{\overset{13}{}}}\frac{x^2}{x-3}dx?$

${\displaystyle \underset{4}{\overset{13}{}}}\frac{x^2}{x-3}dx=$