Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Use the Table of Integrals on Reference Pages 6-10 to evaluate the integral. $ \displaystyle \int \frac{\arctan \sqrt{x}}{\sqrt{x}}\ dx $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$2 \sqrt{x} \arctan \sqrt{x}-\ln (1+x)+C$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 6

Integration Using Tables and Computer Algebra Systems

Integration Techniques

Missouri State University

Campbell University

Oregon State University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

03:35

Use the Table of Integrals…

02:40

03:15

04:26

02:34

02:26

02:41

04:18

Use the Table of Integral…

02:43

02:06

02:48

02:16

03:56

Okay, This question wants us to calculate this integral using the tape. So what we should do is find a way to get this into a form that we know the integral of. So let's make the obvious U substitution. Oh, squared of X because that's the only choice we really have for use up. So that means that do you is equal to one over to root ex d X, but we only have one over rude ex So two d u is equal to one over two rejects. Sorry, just just one DX. So now we have two times the integral of tan in verse. Have you? Do you? And we know the anti derivative of that from the table. So it's you 10 and verse you minus 1/2 the natural log both one plus U squared plus C, and this simplifies to two squared of X Times 10 and verse of spirit of X minus two times 1/2 which is one times the natural log of one plus U squared, which is Route X squared. So ex plus C

View More Answers From This Book

Find Another Textbook

Numerade Educator