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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Integration Using Technology In Exercises 61 and 62, use a symbolic integration utility to find the indefinite integral. Verify the result by differentiating.

1 x  +  x   +   1   d x

To determine

To calculate: The value of the provided indefinite integral 1x+x+1dx using symbolic

integral utility.

Explanation

Given Information:

The provided indefinite integral is 1x+x+1dx.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

undu=un+1n+1+C,

where n1

Calculation:

Consider the indefinite integral say I,

I=1x+x+1dx

Multiply and divide by the conjugate of the denominator that is (xx+1),

I=1x+x+1(xx+1)(xx+1)dx=1(xx+1)(x+x+1)(xx+1)dx=(xx+1)x(x+1)dx=(x+x+1)dx

Now, apply the general power rule for integrtion in the above equation,

I=x12+112+1+(x+1)12+112+1=x3232+(x+1)3232+C=23x32+23(x+1)32+C

Therefore, the value of the provided integral 1x+x+1dx is 23x32+23(x+1)32+C

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