Answer
$$\frac{-3(8^{-x})}{\ln 8} -5\sin x- x\ln x+x+c$$
Work Step by Step
Given $$
\int\left[\frac{3}{8^{x}}-5 \cos x-\ln x\right] d x
$$
Thus:
\begin{align*}
\int\left[\frac{3}{8^{x}}-5 \cos x-\ln x\right] d x&=\int\left[ (3) 8^{-x}-5 \cos x-\ln x\right] d x\\
&=\frac{-3(8^{-x})}{\ln 8} -5\sin x- (x\ln x-x)+c\\
&= \frac{-3(8^{-x})}{\ln 8} -5\sin x- x\ln x+x+c
\end{align*}
