9. Find these indefinite integrals (don't forget the $+C$ where appropriate)
i. (5 points) $\int\left(3 x^{2}+\frac{3}{x}+5 \sec ^{2} x+\frac{2}{x^{3}}\right) d x$
ii. (5 points) $\int\left(3 \cos x+2 e^{2 x}+4^{x}\right) d x$

Step 1 ：Given the integral \(\int\left(3 x^{2}+\frac{3}{x}+5 \sec ^{2} x+\frac{2}{x^{3}}\right) d x\), we can integrate each term separately.

Step 2 ：The integral of \(3x^{2}\) is \(x^{3}\).

Step 3 ：The integral of \(\frac{3}{x}\) is \(3\log(x)\).

Step 4 ：The integral of \(5 \sec ^{2} x\) is \(5\tan(x)\).

Step 5 ：The integral of \(\frac{2}{x^{3}}\) is \(-\frac{1}{x^{2}}\).

Step 6 ：Adding these together and including the constant of integration, we get \(\boxed{x^{3} + 3\log(x) + 5\tan(x) - \frac{1}{x^{2}} + C}\) as the indefinite integral of the given function.

Step 7 ：Given the integral \(\int\left(3 \cos x+2 e^{2 x}+4^{x}\right) d x\), we can integrate each term separately.

Step 8 ：The integral of \(3\cos(x)\) is \(3\sin(x)\).

Step 9 ：The integral of \(2e^{2x}\) is \(e^{2x}\).

Step 10 ：The integral of \(4^{x}\) is \(\frac{4^{x}}{2\log(2)}\).

Step 11 ：Adding these together and including the constant of integration, we get \(\boxed{\frac{4^{x}}{2\log(2)} + e^{2x} + 3\sin(x) + C}\) as the indefinite integral of the given function.