A company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by \( E^{\prime}(x)=12 x+10 \), where \( x \) is the number of days since the start of the job. Find the expenditure if the job takes 4 days.

Evaluate the indefinite integral \( \int 5 \sin ^{4} x \cos x d x= \)

Integrate \( \int_{-2}^{2} 24(6 x-3)^{3} d x \) Answer \( =\square \)

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. \( \int_{0}^{1} \sqrt{1 x+3} d x \)

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