   Chapter 5.2, Problem 21E ### 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. ∫ t t 2   +   6   d t

To determine

To calculate: The value of the provided indefinite integral tt2+6dt.

Explanation

Given Information:

The provided indefinite integral is tt2+6dt.

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=tt2+6dt

Above integral can be written in rational exponent form as;

I=t(t2+6)12dt

Multiply and divide by 2 in the right-hand side of above integral;

I=1(2)(2t)(t2+6)12dt

Take the factor 12 out of the integrand;

I=12(2t)(t2+6)12dt

Let

t2+6=u … (1)

Differentiate the above equation with respect to t;

ddt(t2+6)=dudtddt(t2)+ddt(6)=dudt2t=dudt

Or

(2t)dt=du</

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