Open In App

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 5: Q 43. (page 429)

Solve the integral: $\int \frac{3 x + 1}{x} d x$

Short Answer

Expert verified

The required answer is $3 x + \ln (x) + c$ .

Step by step solution

Step 1. Given information

We have given integral is $\int \frac{3 x + 1}{x} d x$ .

Step 2. Solve the integration by parts .

We have,

$\int \frac{3 x + 1}{x} d x = \int (3 + \frac{1}{x}) d x = \int 3 d x + \int \frac{1}{x} d x = 3 x + \ln (x) + c$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Full access for only 35 $ / year

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve the integral: $\int x \cos (x) d x$ .

True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The substitution x = 2 sec u is a suitable choice for solving $\int \frac{1}{x^{2} - 4} d x$ .

(b) True or False: The substitution x = 2 sec u is a suitable choice for solving $\int \frac{1}{\sqrt{x^{2} - 4}} d x$ .

(d) True or False: The substitution x = 2 sin u is a suitable choice for solving $\int {(x^{2} + 4)}^{- 5 / 2} d x$

(e) True or False: Trigonometric substitution is a useful strategy for solving any integral that involves an expression of the form $\sqrt{x^{2} - a^{2}}$ .

(f) True or False: Trigonometric substitution doesn’t solve an integral; rather, it helps you rewrite integrals as ones that are easier to solve by other methods.

(g) True or False: When using trigonometric substitution with $x = a \sin u$ , we must consider the cases $x > a$ and $x < - a$ separately.

(h) True or False: When using trigonometric substitution with $x = a s e c u$ , we must consider the cases $x > a$ and $x < - a$ separately.

Solve given definite integrals.

$\int_{0}^{4} x \sqrt{x^{2} + 4} d x$

Solve the integral: $\int \frac{x^{2} + 1}{e^{x}} d x$

Solve given definite integral.

$\int_{- 1}^{1} x^{3} \sqrt{9 x^{2} - 1} d x$

See all solutions

Recommended explanations on Math Textbooks

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free

Solve the integral: $\int \frac{3 x + 1}{x} d x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the integration by parts .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Pure Maths

Logic and Functions

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Company

Product

Help

Solve the integral:∫3x+1xdx

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the integration by parts .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Pure Maths

Logic and Functions

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Solve the integral: $\int \frac{3 x + 1}{x} d x$