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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 indefinite integrals In Exercises 31–46, use any basic integration formula or formulas to find the indefinite integral. State which integration formula(s) you used to find the integral.

e 5 x 3 e 3 x + e x e 3 x d x

To determine

To calculate: The indefinite integral e5x3e3x+exe3xdx.

Explanation

Given Information:

The provided indefinite integral is e5x3e3x+exe3xdx.

Formula used:

The general exponent rule of integrals:

eududxdx=eu+C

The constant rule of integrals:

cdu=cdu

Calculation:

Consider the indefinite integral:

e2x+2ex+1exdx

Now, simplify the integrand,

e5x3e3x+exe3xdx=(e5xe3x3e3xe3x+exe3x)dx=(e2x3+e2x)dx=(e2x)dx3dx+e2xdx

Rewrite the integrand as:

∫<

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