Explanation Given: Integral expression as ∫ x a r c csc ( x 2 + 1 ) d x . Formula used: Using formula 80 from the table of integrals: ∫ a r c csc u d u = u a r c csc u + ln | u + u 2 − 1 | + C Calculation: Considering the forms involving inverse trigonometric functions: Use Formula 80 ∫ a r c csc u d u = u a r c csc u + ln | u + u 2 − 1 | + C Let u = x 2 + 1 . Then d u = 2 x d x , get: ∫ x a r c csc ( x 2 + 1 ) d x = 1 2 ∫ a r c csc ( x 2 + <

7th Edition

ISBN: 9781337553032

Author: Larson, Ron, Edwards, Bruce H.

Publisher: Cengage Learning,

See similar textbooks

Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Videos

Question

Chapter 8.7, Problem 19E

To determine

To calculate: The value of the indefinite integral ∫xarccsc(x2+1)dx using the table of integrals.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.7, Problem 18E

Chapter 8.7, Problem 20E

Students have asked these similar questions

Early Monday morning, the temperature in the lecture hall has fallen to 40°F, the same as the temperature outside. At 7:00 A.M., the janitor turns on the furnace with the thermostat set at 72°F. The time constant for the building is = 3 hr and that for the building along with its heating system is 1 K A.M.? When will the temperature inside the hall reach 71°F? 1 = 1 hr. Assuming that the outside temperature remains constant, what will be the temperature inside the lecture hall at 8:30 2 At 8:30 A.M., the temperature inside the lecture hall will be about (Round to the nearest tenth as needed.) 1°F.

Find the absolute extrema of the function f(x, y) = x² + y² - 3x-3y+3 on the domain defined by x² + y² <9. Round answers to 3 decimals or more. Absolute Maximum: Absolute Minimum:

Find the maximum and minimum values of the function f(x, y) = e² subject to ï³ + y³ = 128 Please show your answers to at least 4 decimal places. Enter DNE if the value does not exist. Maximum value:

Chapter 8 Solutions

Calculus

Ch. 8.1 - CONCEPT CHECKS Integration Technique Describe how...Ch. 8.1 - CONCEPT CHECK Fitting Integrands to Basic...Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing an Antiderivative In Exercises 3 and 4,...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, selectthe...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The value of the indefinite integral ∫ x a r c csc ( x 2 + 1 ) d x using the table of integrals.

Solution Summary: The author explains how to calculate the value of the indefinite integral using the table of integrals.

Concept explainers

Videos

To calculate: The value of the indefinite integral ∫xarccsc(x2+1)dx using the table of integrals.

Want to see the full answer?

Chapter 8 Solutions