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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find f.

f″(x) = 2x + 3ex

To determine

To find: The general antiderivative for the function f(x)=2x+3ex .

Explanation

Given Data:

Write the given function as follows.

f(x)=2x+3ex

Formula used:

The antiderivative function for the function xn is xn+1n+1+C .

Here, C is the constant.

The antiderivative function for the function ex is ex+C .

Calculation of f(x) :

Write the function as follows.

f(x)=2x1+3ex (1)

From the antiderivative function formula, the antiderivative for the function in equation (1) is written as follows.

f(x)=2(x1+11+1)+3ex+C=2(x22)+3ex+C=x2+3ex+C

Calculation of f(x) :

Rewrite the function f(x)=x2+3ex+C as follows

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