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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) = x6 − 4x4 + x + 1

To determine

To find: The general antiderivative for the function f(x)=x64x4+x+1 .

Explanation

Given Data:

Write the given function as follows.

f(x)=x64x4+x+1

Formula used:

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

Here, C is the constant.

Calculation of f(x) :

Rewrite the function f(x)=x64x4+x+1 as follows.

f(x)=x64x4+x1+1x0 (1)

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

f(x)=x6+16+14(x4+14+1)+x1+11+1+x0+10+1+C=x774(x55)+x22+x+C=17x745x5+12x2+x+C

Calculation of f(x) :

Rewrite the function f(x)=17x745x5+12x2+x+C as follows.

f(x)=17x745x5+12x2+x1+Cx0 (2)

From the antiderivative function formula, the antiderivative for the function in equation (2) is written as follows

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