Question Find the most general antiderivative (including the constant term, \( C), F(x) \) given the function below. \[ f(x)=\tan (x)(4 \cos (x)+8 \sec (x)) \] Provide your answer below: \( F(x)=\square \)

Given two sequences \( \left\{a_{n}\right\} \) and \( \left\{b_{n}\right\} \) : \[ \begin{aligned} a_{n} & =\frac{2 n}{n+1} \\ b_{n} & =\frac{1}{n^{2}}\end{aligned} \]

Evaluate the indefinite integral. \( \int x^{2} \sqrt{15+x^{3}} d x \) \( \square+C \)

Evaluate the indefinite integral. \( \int 8 \sin ^{3}(x) \cos (x) d x=\square+C \)

Evaluate the integral by making the appropriate substitution: \( u=\square \frac{d x}{(2 x+2)^{4}} \), \( \int \frac{d x}{(2 x+2)^{4}}=\square \)

Evaluate the definite integral. \( \int_{0}^{1} \sqrt{1 x+3} d x \)