   Chapter 12.2, Problem 25E ### 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

# Evaluate the integrals in Problems 7-36. Check your results by differentiation. ∫ ( 3 x 4 − 1 ) 2 12 x   ​ d x

To determine

To calculate: The value of the integral (3x41)212xdx and also check the solution by differentiation.

Explanation

Given Information:

The provided integral is (3x41)212xdx.

Formula used:

According to the power formula of integrals, if u=u(x), then,

undu=un+1n+1+C

According to the power rule of derivative,

ddx(xn)=nxn1

Calculation:

Consider the provided integral,

(3x41)212xdx

Now, let 3x41=u

Differentiate 3x41=u with respect to x and get,

12x3dx=du

Here, this substitution does not work.

Hence, this method fails.

So, simplify the integrand algebraically as,

(3x41)212xdx=(9x86x4+1)12xdx=(108x972x5+12x)dx

Use the power rule of integrals,

undu=un+1n+1+C

Now, integrate the above expression with respect to x

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