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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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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.

6 x ( 3 x 2  - 5) 4   d x

To determine

To calculate: The value of the provided indefinite integral 6x(3x25)4dx.

Explanation

Given Information:

The provided indefinite integral is 6x(3x25)4dx.

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=6x(3x25)4dx

Let

3x25=u … (1)

Differentiate the above equation with respect to x;

ddx(3x25)=dudxddx(3x2)ddx(5)=dudx(6x)=dudx

Or

(6x)dx=du … (2)

Substitute the values of 3x25 and (6x)dx from equations (1) and (2) respectively in the provided integral;

I=1u4du

Use the identity am=1am in the above integral;

I=

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