91Ó°ÊÓ

Find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) $$ \int x^{4} \ln x d x $$

Find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) $$ \int \frac{e^{1 / t}}{t^{2}} d t $$

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. $$ \int_{0}^{9} \frac{1}{\sqrt{9-x}} d x $$

Present Value In Exercises 25 and 26, use a program similar to the Simpson's Rule program on page 906 with \(n=8\) to approximate the present value of the income \(c(t)\) over \(t_{1}\) years at the given annual interest rate \(r\). Then use the integration capabilities of a graphing utility to approximate the present value. Compare the results. (Present value is defined in Section 12.1.) $$ c(t)=6000+200 \sqrt{t}, r=7 \%, t_{1}=4 $$

Use partial fractions to find the indefinite integral. $$ \int \frac{x^{2}-4 x-4}{x^{3}-4 x} d x $$

Use partial fractions to find the indefinite integral. $$ \int \frac{x^{2}+12 x+12}{x^{3}-4 x} d x $$

Present Value In Exercises 25 and 26, use a program similar to the Simpson's Rule program on page 906 with \(n=8\) to approximate the present value of the income \(c(t)\) over \(t_{1}\) years at the given annual interest rate \(r\). Then use the integration capabilities of a graphing utility to approximate the present value. Compare the results. (Present value is defined in Section 12.1.) $$ c(t)=200,000+15,000 \sqrt[3]{t}, r=10 \%, t_{1}=8 $$

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. $$ \int_{0}^{2} \frac{x}{\sqrt{4-x^{2}}} d x $$

Find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) $$ \int \frac{1}{x(\ln x)^{3}} d x $$

Find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) $$ \int x(\ln x)^{2} d x $$