Question: "Evaluate the integral. ∫dxx2+2x+10" - Plainmath

BolkowN

Answered question

2021-11-09

Evaluate the integral.

\int \frac{d x}{x^{2} + 2 x + 10}

Answer & Explanation

likvau

Skilled2021-11-10Added 75 answers

Given,

\int \frac{d x}{x^{2} + 2 x + 10}

Now consider,

x^{2} = 2 x + 10 = x^{2} + 2 x + 1 + 9

= {(x + 1)}^{2} + 3^{2}

Therefore given integral becomes,

\int \frac{d x}{x^{2} + 2 x + 10} = \int \frac{d x}{{(x + 1)}^{2} + 3^{2}}

= \frac{1}{3} \tan^{- 1} (\frac{x + 1}{3}) + C [∵ \int \frac{d x}{x^{2} + a^{2}} = \frac{1}{a} \tan^{- 1} (\frac{x}{a}) + C]

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