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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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Finding an Indefinite Integral In Exercises 17-38, find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.)

( 2 x 1 ) e 7 x d x

To determine

To calculate: The value of indefinite integral (2x1)e7xdx.

Explanation

Given Information:

The provided indefinite integral is (2x1)e7xdx.

Formula used:

Integration Property:

eaxdx=eaxa+C

Calculation:

Consider the indefinite integral (2x1)e7xdx

Here,

dv=e7xdx and u=2x1

First find v,

dv=e7xdxdv=e7xdx

On further solving,

v=e7x7 …...…... (1)

Now find du,

u=(2x1)

Differentiate both side with respect x,

dudx=d(2x1)dxdudx=2

And,

du=2dx …...…... (2)

Apply integration by parts formula and substitute equation (1) and (2) in udv=uvvdu,

(2x1)e7xdx=17(2x1)e7x27e7xdx

Apply the formula eaxdx=<

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