Get the solution to "Find the indefinite integral of ∫x2x−9dx"

Daniaal Sanchez

Answered question

2021-11-06

Find the indefinite integral of

\int \frac{x^{2}}{x - 9} d x

tabuordg

Skilled2021-11-07Added 99 answers

Step 1
To evaluate

\int \frac{x^{2}}{x - 9} d x

Step 2
Now substitute x - 9 = u, x = u+9
And dx = du
Step 3
Now substitute the value of x and dx in above integral, we get

\int \frac{{(u + 9)}^{2}}{u} d u

Step 4
Now simplify the above integral, we get

\int \frac{{(u + 9)}^{2}}{u} d u = \int \frac{u^{2} + 18 u + 81}{u} d u

= \int (u + 18 + \frac{81}{u}) d u

= \frac{u^{2}}{2} + 18 u + 81 \ln | u | + c

Step 5
Now replace u = x-9, we get

\int \frac{x^{2}}{x - 9} d x = \frac{{(x - 9)}^{2}}{2} + 18 (x - 9) + 81 \ln | x - 9 | + c

Step 6
Answer:

\int \frac{x^{2}}{x - 9} d x = \frac{{(x - 9)}^{2}}{2} + 18 (x - 9) + 81 \ln | x - 9 | + c

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