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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 by Substitution In Exercises 35–42, use the method of substitution to find the indefinite integral. Check your result by differentiating. See Examples 6 and 7.

t t 2 + 1 d t

To determine

To calculate: The indefinite integral of tt2+1 dt and to check the result by differentiating.

Explanation

Given Information:

The provided expression is, tt2+1 dt.

Formula used:

General Power Rule:

If u is a differentiable function of x, then

undudxdx=undu=un+1n+1+c,n1

The Constant Multiple Rule:

ddxcf(x)=cf(x)

The Chain Rule:

ddxf(g(x))=f(g(x))g(x)

The Power Rule:

ddxxn=nxn1

Where n is a real number.

Calculation:

Consider the expression, tt2+1 dt.

Let u=t2+1,

So,

du=2t dt12dudt=t

Now use the general power rule to get,

12(u)12 du

Now the integral will be:

12u12+112+1+C=12u3232+C=1223u32+C=13u32+C

Substitute back the value of u

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