   Chapter 12.1, Problem 30E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 29-32, use algebra to rewrite the integrands; then integrate and simplify. ∫ ( x 3 + 1 ) 2 x   d x

To determine

To calculate: The value of the integral (x3+1)2xdx.

Explanation

Given Information:

The provided integral is (x3+1)2xdx

Formula used:

The algebraic identity:

(a+b)2=a2+2ab+b2

The properties of integrals:

[u(x)±v(x)]dx=u(x)dx±v(x)dx.

The power formula of integrals:

xndx=xn+1n+1+C (forn1)

The power rule of differentiation:

ddx(xn)=nxn1

The properties of integrals:

dx=x+C

Calculation:

Consider the provided integral:

(x3+1)2xdx

Now, use the algebraic identity:

(a+b)2=a2+2ab+b2

To simplify the integrand as:

(x3+1)2xdx=(x6+2x3+1)xdx=(x7+2x4+x)dx

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