Consider the integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{11}\sqrt[\phantom{2}]{x^6-10}dx.$

To find the value of this integral, make the substitution $u=$

Then, $du=$

Substituting just these two these into the integral, we have

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{6}{x}^6\sqrt[\phantom{2}]{u}du$

At this stage, are you ready to find the antiderivative?

yes

$$ no

Re$-$write $x^6$ in terms of $u$:$x^6=$

Subbing this in$,$ we find that ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{11}\sqrt[\phantom{2}]{x^6-10}dx$

$={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}du$

$$

$+C$

$+C$