91Ó°ÊÓ

Find each indefinite integral. $$ \int(1-7 w) \sqrt[3]{w} d w $$

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. \(f(x)=\frac{1}{x^{2}}\) from \(x=1\) to \(x=3\)

Find each indefinite integral by the substitution method or state that it cannot be found by our substitution formulas. $$ \int\left(3 y^{2}-6 y\right)^{3}(y-1) d y $$

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. \(f(x)=8-4 \sqrt[3]{x}\) from \(x=0\) to \(x=8\)

ENVIRONMENTAL SCIENCE: Pollution The amount of pollution in a lake \(x\) years after the closing of a chemical plant is \(P(x)=100 / x\) tons (for \(x \geq 1\) ). Find the average amount of pollution between 1 and 10 years after the closing.

Find each indefinite integral. $$ \int \frac{6 x^{3}-6 x^{2}+x}{x} d x $$

Find each indefinite integral. \(\int \frac{z^{3}+z}{z^{2}} d z\)

Find each indefinite integral by the substitution method or state that it cannot be found by our substitution formulas. $$ \int e^{x^{2}+2 x+5}(x+1) d x $$

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. \(f(x)=9-3 \sqrt{x}\) from \(x=0\) to \(x=9\)

Find each indefinite integral. \(\int \frac{z^{2}+1}{z} d z\)