Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Problem 33
Evaluate the integrals. Some integrals do not require integration by parts. $$ \int x(\ln x)^{2} d x $$
Problem 33
The integrals in Exercises \(1-34\) converge. Evaluate the integrals without using tables. $$\int_{-1}^{\infty} \frac{d \theta}{\theta^{2}+5 \theta+6}$$
Problem 33
In Exercises \(33-38,\) perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. $$ \int \frac{2 x^{3}-2 x^{2}+1}{x^{2}-x} d x $$
Problem 33
Use any method to evaluate the integrals in Exercises \(15-34 .\) Most will require trigonometric substitutions, but some can be evaluated by other methods. $$ \int \frac{v^{2} d v}{\left(1-v^{2}\right)^{5 / 2}} $$
Problem 33
In Exercises \(27-40\) , use a substitution to change the integral into one
you can find in the table. Then evaluate the integral.
$$
\int \cot t \sqrt{1-\sin ^{2} t} d t, \quad 0
Problem 34
Evaluate the integrals. Some integrals do not require integration by parts. $$ \int \frac{1}{x(\ln x)^{2}} d x $$
Problem 34
In Exercises \(27-40\) , use a substitution to change the integral into one you can find in the table. Then evaluate the integral. $$ \int \frac{d t}{\tan t \sqrt{4-\sin ^{2} t}} $$
Problem 34
Use any method to evaluate the integrals in Exercises \(15-34 .\) Most will require trigonometric substitutions, but some can be evaluated by other methods. $$ \int \frac{\left(1-r^{2}\right)^{5 / 2}}{r^{8}} d r $$
Problem 34
In Exercises \(33-38,\) perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. $$ \int \frac{x^{4}}{x^{2}-1} d x $$
Problem 34
Car accidents The number of days that elapse between the beginning of a calendar year and the moment a high-risk driver is involved in an accident is exponentially distributed. Based on historical data, an insurance company expects that 30\(\%\) of high-risk drivers will be involved in an accident during the first 50 days of the calendar year. In a group of 100 high-risk drivers, how many do you expect to be involved in an accident during the first 80 days of the calendar year?
