Key to "Determine the following indefinite integral. ∫x2−36x−6dx"

High School
Calculus and Analysis
Calculus 2
Applications of integrals

namenerk

Answered question

2021-12-14

Determine the following indefinite integral.

\int \frac{x^{2} - 36}{x - 6} d x

Answer & Explanation

Matthew Rodriguez

Beginner2021-12-15Added 32 answers

Step 1
We have to determine the following indefinite integral.
$\int \frac{x^{2} - 36}{x - 6} d x$
Step 2
$\int \frac{x^{2} - 36}{x - 6} d x = \int \frac{x^{2} - 6^{2}}{x - 6} d x$
$= \int \frac{(x - 6) (x + 6)}{x - 6} d x$
$= \int (x + 6) d x$
$= \frac{x^{2}}{2} + 6 x + c o n s t a n t$
the required answer is
$\int \frac{x^{2} - 36}{x - 6} d x = \frac{x^{2}}{2} + 6 x + c o n s t a n t$
now, we check the answer by differentiation
$\frac{d}{d x} (\frac{x^{2}}{2} + 6 x + c o n s \tan t) = \frac{2 x}{2} + 6$
=x+6
$\Rightarrow \frac{d}{d x} (\frac{x^{2}}{2} + 6 x + c o n s \tan t) = \frac{(x + 6) (x - 6)}{x - 6} = \frac{x^{2} - 36}{x - 6}$

Pansdorfp6

Beginner2021-12-16Added 27 answers

Lets

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 2

Didn't find what you were looking for?