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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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Using Integration Tables In Exercises 1–8, use the indicated formula from the integration table in Appendix C to find the indefinite integral. See Examples 1, 2, and 3.

x 1 + e x 2 d x , Formula 39

To determine

To calculate: The solution of indefinite integral x1+ex2dx.

Explanation

Given Information:

The integral is x1+ex2dx.

Formula used:

The formula 39 form the appendix C is,

11+eudu=uln(1+eu)+C.

General power differentiation Rule,

ddx[un]=nun1dudx

Calculation:

Let u=x2.

Differentiate the above equation with respect to x,

du=2xdx

Consider the provided integral,

x1+ex2dx

Multiply and divide by 2.

x1+ex2dx=122x1+ex2dx=1211+ex22xdx

Substitute u for x2, and du for 2xdx

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