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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.

x 2 + 2 x + 5 x 1 d x

To determine

To calculate: The indefinite integral x2+2x+5x1dx.

Explanation

Given Information:

The provided indefinite integral is x2+2x+5x1dx.

Formula used:

The general logarithmic rule of integrals:

1ududxdx=ln|u|+C

The general power rule of integration:

undu=un+1n+1+C

The constant rule of integration:

cdu=cu+C

Calculation:

Consider the indefinite integral:

x2+2x+5x1dx

Rewrite the integrand as:

x2+2x+5x1dx=x2+3xx3+8x1dx=x(x+3)1(x+3)+8x1dx=(x+3)(x1)+8x1

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