$\int_{0}^{\frac{1}{6}}\frac{1}{\sqrt{1-(3x)^{2}}}dx$

What trig derivative do you recognize?

Refer to the hint in part (a).
Also, remember that 4x² = (2x)²

$=\frac{1}{3\ln 2}2^{3x}\Big|_0^1=\frac{7}{3\ln 2}$

This integral is very much like that in part (c).