   Chapter 5.2, Problem 62E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### 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. ∫ x 3 x  + 2 d x

To determine

To calculate: The value of the provided indefinite integral x3x+2dx using symbolic

integral utility.

Explanation

Given Information:

The provided indefinite integral is x3x+2dx.

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=x3x+2dx …… (1)

Let 3x+2=u

Differentiate the equation with respect to x,

ddx(3x+2)=dudx3ddx(x)+ddx(2)=dudx3+0=dudx3dx=du

Divide by 3 on both sides,

dx=13du

And 3x+2=u

Subtract 2 from both sides,

3x+22=u23x=u2

Divide by 3 on both sides,

3x3=u23x=u23

Substitute the value of dx=13du, 3x+2=u and x=u23 in the equation (1),

I=u29udu=19(u122u12)du

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

I=19((u12+112+1)2(u12+112+1))+C=19u323229u1212+C=227u3249u12+C

Now substitute 3x+2 for u in the above equation,

I=227(3x+2)32493x+2+C

Therefore, the value of the provided integral x3x+2dx is 227(3x+2)32493x+2+C

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