   Chapter 8.1, Problem 4E

Chapter
Section
Textbook Problem
1 views

# Choosing an Antiderivative In Exercises 1–4, select the correct antiderivative. d y d x =   x cos ( x 2 + 1 ) (a) 2 x sin ( x 2 + 1 ) + c (b) − 1 2 sin ( x 2 + 1 ) + c (c) 1 2 sin ( x 2 + 1 ) + c (d) − 2 x sin ( x 2 + 1 ) + c

To determine

To calculate: The value of anti-derivative of dydx=xcos(x2+1) and choose the correct option from the following:

(a)2xsin(x2+1)+C(b)12sin(x2+1)+C(c)12sin(x2+1)+C(d)2xsin(x2+1)+C

Explanation

Given:

The provided expression is dydx=xcos(x2+1).

Formula used:

The cosine rule is cos(u)du=sinu+C.

Calculation:

Consider the function dydx=xcos(x2+1).

Take the x variables on one side and y variables on the other side.

dy=xcos(x2+1)dx

Take integration sign on both sides.

dy=xcos(x2+1)dx …… (1)

Substitute.

First let’s assume that x2+1=t …… (2)

Differentiate both sides with respect to x.

2xdx=dt

Take x terms on one side and the constant and t terms on the other side

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 