/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 41 Use a symbolic integration utili... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 41

Use a symbolic integration utility to find the indefinite integral. $$ \int(x+1)(3 x-2) d x $$

Short Answer

Expert verified
The indefinite integral of the function \( (x+1)(3x-2) \) is \( x^3 + \frac{x^2}{2} - 2x + C \)

Step by step solution

01

Expand the integrand

Start by expanding the product within the integrand to simplify the integral. It results in: \[ \int x(3x-2) + 1(3x-2) dx = \int (3x^2 - 2x + 3x - 2) dx \] which further simplifies to: \[ \int (3x^2 + x - 2) dx \]
02

Separate integrals according to terms

Separate the integral to different terms which makes it easier to integrate: \[ \int 3x^2 dx + \int x dx - \int 2 dx \]
03

Integrate each term separately

Next, integrate each of these terms separately: \[ \frac{3}{3} \int x^2 dx + \frac{1}{2} \int 2x dx - 2 \int dx = x^3 + \frac{x^2}{2} - 2x + C \], where C is the constant of integration.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

The velocity \(v\) of the flow of blood at a distance \(r\) from the center of an artery of radius \(R\) can be modeled by \(v=k\left(R^{2}-r^{2}\right), \quad k>0\) where \(k\) is a constant. Find the average velocity along a radius of the artery. (Use 0 and \(R\) as the limits of integration.)

Use the Trapezoidal Rule with \(n=10\) to approximate the area of the region bounded by the graphs of the equations. $$ y=x \sqrt{\frac{4-x}{4+x}}, \quad y=0, \quad x=4 $$

Use a graphing utility to graph the region bounded by the graphs of the functions, and find the area of the region. $$ f(x)=3-2 x-x^{2}, g(x)=0 $$

Use the Midpoint Rule with \(n=4\) to approximate the area of the region. Compare your result with the exact area obtained with a definite integral. $$ f(x)=1-x^{2}, \quad[-1,1] $$

Sketch the region bounded by the graphs of the functions and find the area of the region. $$ y=\frac{8}{x}, y=x^{2}, y=0, x=1, x=4 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.