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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 25–36, find the indefinite integral. Check your result by differentiating. See Examples 4 and 5.

2 x 3 1 x 3 d x

To determine

To calculate: The value of indefinite integral (2x31x3)dx and check the result by differentiation.

Explanation

Given Information:

The indefinite integral is (2x31x3)dx.

Formula used:

The simple power rule of integration, xndx=xn+1n+1+C where, n1.

The sum or difference rule of integration, (f(x)±g(x))dx=f(x)dx±g(x)dx.

The simple power rule for the derivative, ddx[xn]=nxn1.

Calculation:

Consider the indefinite integral (2x31x3)dx.

The integrand of the indefinite integral is (2x31x3).

Integrate the provided indefinite integral use the sum or difference rule of integration, (f(x)±g(x))dx=f(x)dx±g(x)dx.

(2x31x3)dx=2x3x3dx1x3dx=2dxx3dx=2dxx3dx

Integrate further use the simple power rule of integration, xndx=xn+1n+1+C

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