"Use integration tables to find or evaluate the..." was answered by students like you

facas9

Answered question

2021-11-05

Use integration tables to find or evaluate the integral.

\frac{x}{x^{2} + 4 x + 8} d x

Szeteib

Skilled2021-11-06Added 102 answers

Step 1
We have to evaluate the following integral:

\frac{x}{x^{2} + 4 x + 8} d x

Step 2
Then we get,

\frac{x}{x^{2} + 4 x + 8} d x

= \frac{1}{2} \int \frac{2 x}{x^{2} + 4 x + 8} d x

= \frac{1}{2} \int (\frac{2 x + 4}{x^{2} + 4 x + 8}) d x - \frac{1}{2} \int \frac{4 d x}{x^{2} + 4 x + 8}

= \frac{1}{2} \ln | x^{2} + 4 x + 8 | - 2 \times \frac{1}{2} \tan^{- 1} (\frac{x + 2}{2}) + C

= \frac{1}{2} \ln | x^{2} + 4 x + 8 | - \tan^{- 1} (\frac{x + 2}{2}) + C

where C is the constant of integration
Hence the answer.

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