91Ó°ÊÓ

These exercises review material that will be helpful in Section \(5.6\). Find the derivative of each function. \(\ln \left(x^{4}+1\right)\)

Find each indefinite integral by the substitution method or state that it cannot be found by our substitution formulas. \(\int \frac{x^{3}+x^{2}}{\left(3 x^{4}+4 x^{3}\right)^{2}} d x\)

Find each indefinite integral. \(\int(r-1)(r+1) d r\)

Use a definite integral to find the area under each curve between the given \(x\) -values. For Exercises 19-24, also make a sketch of the curve showing the region. \(f(x)=6 e^{2 x}\) from \(x=0\) to \(x=2\)

Find each indefinite integral. \(\int(3 s+1)(3 s-1) d s\)

Find each indefinite integral by the substitution method or state that it cannot be found by our substitution formulas. \(\int \frac{x^{2}-x}{\left(2 x^{3}-3 x^{2}\right)^{3}} d x\)

Sales of Apple Macintosh computers in recent years have been approximately \(S(x)=2 x^{2}-9 x+39\) hundred thousand units, where \(x\) is the number of years since 2000 . Find the average sales from 2000 to 2006 .

These exercises review material that will be helpful in Section \(5.6\). Find the derivative of each function. \(\ln \left(x^{3}-1\right)\)

Find each indefinite integral. [Hint: Use some algebra first.] \(\int \frac{(x-1)^{2}}{x} d x\)

These exercises review material that will be helpful in Section \(5.6\). Find the derivative of each function. \(e^{x^{3}}\)