Question
Integrate the following functions w.r.t. x:
$\frac{x^2}{\sqrt{9-x^6}}$
$\frac{x^2}{\sqrt{9-x^6}}$
Put $x^3=t \quad \therefore 3 x^2 d x=d t \quad \therefore x^2 d x=\frac{1}{3} d t$
$\therefore I=\int \frac{1}{\sqrt{9-t^2}} \cdot \frac{d t}{3}$
$\begin{aligned} & =\frac{1}{3} \int \frac{d t}{\sqrt{3^2-t^2}} \\ = & \frac{1}{3} \sin ^{-1}\left(\frac{t}{3}\right)+c \\ = & \frac{1}{3} \sin ^{-1}\left(\frac{x^3}{3}\right)+c .\end{aligned}$
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Show that $\overline{A B}+\overline{A E}+\overline{B C}+\overline{D C}+\overline{E D}=2 \overline{A C}$