Find the indefinite integral. \int\frac{{{x}^{2}-{96}}}{{x}}{\left.{d}{x}\right.}

Albarellak

Albarellak

Answered question

2021-09-01

Find the indefinite integral.
x296xdx

Answer & Explanation

Sally Cresswell

Sally Cresswell

Skilled2021-09-02Added 91 answers

Take the integral:
x296xdx
For the integrand x296x, expand out the fraction:
=x96xdx
INTERMEDIATE STEPS:
Expand the following:
=x96xdx
Hint: Express x296x as a difference of fractions.
x296x=x2x96x:
x2x96x
Hint: For all exponents, anam=anm. Apply this to x2x.
Combine powers. x2x=x21:
x2196x
Hint: Evaluate 21.
21=1:
Answer: x96x
Integrate the sum term by term and factor out constants:
=xdx961xdx
The integral of x is x22:
=x22961xdx
The integral of 1x is log(x):
Answer:
=x2296log(x)+constant

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