# Evaluate int_0^1 (x^5+x^4+x^2)sqrt(4x^3+5x^2+10)dx

Evaluate
${\int }_{0}^{1}\left({x}^{5}+{x}^{4}+{x}^{2}\right)\sqrt{4{x}^{3}+5{x}^{2}+10}\phantom{\rule{thickmathspace}{0ex}}dx$
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Izabella Henson
$\begin{array}{rl}{\int }_{0}^{1}\left({x}^{5}+{x}^{4}+{x}^{2}\right)\sqrt{4{x}^{3}+5{x}^{2}+10}dx& ={\int }_{0}^{1}\left({x}^{4}+{x}^{3}+x\right)\sqrt{4{x}^{5}+5{x}^{4}+10{x}^{2}}dx\\ & =\frac{1}{20}{\int }_{0}^{19}\sqrt{u}du=\frac{{19}^{3/2}}{30}\end{array}$