Question: "Evaluate the indefinite integral. ∫dxx2+6x+8"

tricotasu

Answered question

2021-10-31

Evaluate the indefinite integral.

\int \frac{d x}{x^{2} + 6 x + 8}

Pohanginah

Skilled2021-11-01Added 96 answers

Step 1: To Find
We have to evaluate the indefinite integral

\int \frac{d x}{x^{2} + 6 x + 8}

Step 2: Calculation

\int \frac{d x}{x^{2} + 6 x + 8} = \int \frac{d x}{(x + 2) (x + 4)}

= \frac{1}{2} \int [\frac{1}{x + 2} - \frac{1}{x + 4}] d x

= \frac{1}{2} [\int \frac{1}{x + 2} d x - \int \frac{1}{x + 4} d x]

= \frac{1}{2} [\ln (x + 2) - \ln (x + 4)] + C ∵ \int \frac{1}{x} d x = \ln x

= \frac{\ln (x + 2)}{2} - \frac{\ln (x + 4)}{2} + C

\int \frac{d x}{x^{2} + 6 x + 8} = \frac{\ln (x + 2)}{2} - \frac{\ln (x + 4)}{2} + C

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