91影视

Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge.\(\int_{0}^{1} \ln x d x\)

Integrate using the method of trigonometric substitution. Express the final answer in terms of the variable. $$ \int \frac{x^{2} d x}{\sqrt{x^{2}-1}} $$

Find the integral by using the simplest method. Not all problems require integration by parts. $$ \int \cos (\ln x) d x $$

Approximate the following integrals using either the midpoint rule, trapezoidal rule, or Simpson's rule as indicated. (Round answers to three decimal places.) \(\int_{0}^{1} \sin ^{2}(\pi x) d x ;\) midpoint rule; \(n=3\)

Use a CAS to evaluate the following integrals. Tables can also be used to verify the answers. $$ \int x^{3} \sin x d x $$

Use an identity to reduce the power of the trigonometric function to a trigonometric function raised to the first power. \(\sin ^{2} x=\) _______

Use a CAS to evaluate the following integrals. Tables can also be used to verify the answers. $$ \int x \sqrt{x^{4}-9} d x $$

Express the rational function as a sum or difference of two simpler rational expressions. \(\frac{2 x}{(x+2)^{2}}\)

Use the midpoint rule with eight subdivisions to estimate \(\int_{2}^{4} x^{2} d x\).

Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge.\(\int_{-2}^{2} \frac{d x}{(1+x)^{2}}\)