   Chapter 4.1, Problem 27E

Chapter
Section
Textbook Problem

Finding an Indefinite Integral In Exercises 15-36, find the indefinite integral and check the result by differentiation. ∫ ( x + 1 ) ( 3 x − 2 ) d x

To determine

To calculate: The solution of the indefinite integral expressed as (x+1)(3x2)dx and check the result by differentiation.

Explanation

Given:

The provided integral is (x+1)(3x2)dx.

Formula used:

The integration of a function xn is given as,

xndx=xn+1n+1+C

The derivative of a function xn is given as,

ddx(xn)=nxn1

And, the derivative of a constant is given as,

ddx(Constant)=0

Calculation:

Consider the given integral expressed as,

(x+1)(3x2)dx

Integrate the expression above to get,

(x+1)(3x2)dx=(3x2+3x2x2)dx=(3x2+x2)dx=3x2dx+xdx2dx=3(x33)+

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