Can someone help me find the integrals for the ff:
$$\int \frac{\sqrt{9z^{2}-1}}{27z^{4}}\,dz$$
$$\int y^{2}\sqrt{25-y^{2}} dy$$
For the second one I have tried to do answer it and this is what I have made:
$x=5\sin(\theta) $
$dx=5\cos(\theta)\,d\theta$
$\int 25\sin^{2}\theta \sqrt{25-25\sin^{2}\theta }\cdot 5\cos\theta\, d\theta$
$625\int \sin^{2}\theta \cos^{2}\theta\, d\theta $
$625\int (1-\cos^{2}\theta ) \sin^{2}\theta \cos^{2}\theta\, d\theta $
and at this point i'm not sure if I did it correct or not.
and
$$\int \frac{dx}{x^{2}{\sqrt{4x^{2}-9}}}$$
Hints:
Take $z=\frac13\sec\theta$
Take $y=5\sin\theta$
Take $x=\frac32\sec\theta$