   Chapter 5.2, Problem 23E ### 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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# Applying the General Power Rule In Exercises 9-34, find the indefinite integral. Check your result by differentiating. See Examples 1, 2, 3, and 5. ∫ x 4 ( 3   −   2 x 5 )   d x

To determine

To calculate: The value of the provided indefinite integral x4(32x5)3dx.

Explanation

Given Information:

The provided indefinite integral is x4(32x5)3dx.

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

And

am=1am

Calculation:

Consider the indefinite integral say I,

I=x4(32x5)3dx

Multiply and divide by -10 in the right-hand side of above integral;

I=1(10)(10x4)(32x5)3dx

Take the factor 110 out of the integrand;

I=110(10x4)(32x5)3dx

Let

32x5=u … (1)

Differentiate the above equation with respect to x;

ddx(32x5)=dudxddx(3)ddx(2x5)=dudx(10x4)=dudx

Or

(10x4)dx=du … (2)

Substitute the values of 32x5 and (10x4)dx from equations (1) and (2) respectively in the provided integral

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