Evaluate the integral

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^3(x^4-10{)}^{18}dx$

$by$ making the substitution $u=x^4-10.$

$+C$

~~ Incorrect! $Be$ sure $to$ use the derivative $ofuto$ find a substitution that $is$ equivalent $to$

$x^{3}dx.$ Since $du=4x^{3}dx,$ you can substitute $\frac{du}{4}$ for $x^{3}dx.$ Now you should $be$ able $to$

rewrite the integral entirely $in$ terms $ofu$ and integrate using the power rule. Afterwards,

don't forget $to$ rewrite the answer back $in$ terms $ofx.$

Note: Your answer should $bein$ terms $ofx$ and not $u.$

Rewrite the integrand $in$ terms $ofuby$ using the given $u-$substitution and the derivative $ofuto$

make a substitution for the remaining parts $of$ the integrand. Then, apply the power rule $to$

evaluate the integral. Finally, rewrite your answer $in$ terms $ofx.$