Expert answers to "Completing the square Evaluate the following integrals. ∫dxx2+6x+18"

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Answered question

2021-10-27

Completing the square Evaluate the following integrals.

\int \frac{d x}{x^{2} + 6 x + 18}

Szeteib

Skilled2021-10-28Added 102 answers

Step 1
The given integral is

\int \frac{d x}{x^{2} + 6 x + 18}

.
Evaluate the above integral as follows.
Step 2

\int \frac{d x}{x^{2} + 6 x + 18} = \int \frac{d x}{{(x + 3)}^{2} - 3^{2} + 18}

= \int \frac{d x}{{(x + 3)}^{2} - 9 + 18}

= \int \frac{d x}{{(x + 3)}^{2} + 9}

= \int \frac{d x}{{(x + 3)}^{2} + 3^{2}}

= \frac{1}{3} \tan^{- 1} (\frac{x + 3}{3}) + C

Thus,

\int \frac{d x}{x^{2} + 6 x + 18} = \frac{1}{3} \tan^{- 1} (\frac{x + 3}{3}) + C

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