Answer: (a) \(2\ln11\). (b) \(\frac{255}{8}e^4\).

(a) Since

\(\int \frac{10}{5x+2}\,dx=2\ln(5x+2),\)

we get

\(\int_0^4 \frac{10}{5x+2}\,dx=\left[2\ln(5x+2)\right]_0^4.\)

Therefore

\(=2\ln22-2\ln2=2\ln\left(\frac{22}{2}\right)=2\ln11.\)

So

\(\boxed{2\ln11}.\)

(b) First simplify the integrand:

\(\left(e^{4x+2}\right)^2=e^{8x+4}.\)

Thus

\(\int_0^{\ln2}\left(e^{4x+2}\right)^2\,dx=\int_0^{\ln2} e^{8x+4}\,dx.\)

Integrating gives

\(\left[\frac18 e^{8x+4}\right]_0^{\ln2}.\)

So

\(=\frac18\left(e^{8\ln2+4}-e^4\right).\)

Since \(e^{8\ln2}=2^8=256\),

\(=\frac18(256e^4-e^4)=\frac{255}{8}e^4.\)

Therefore

\(\boxed{\frac{255}{8}e^4}.\)