Question:
Integrate the function: \(\frac {1}{\sqrt {x^2+2x+2}}\)
Integrate the function: \(\frac {1}{\sqrt {x^2+2x+2}}\)
Updated On: Oct 4, 2023
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Solution and Explanation
\(∫\frac {1}{\sqrt {x^2+2x+2 }}\ dx\) = \(∫\frac {1}{\sqrt {(x+1)^2+(1)^2} }\ dx\)
\(Let \ x+1 = t\)
\(∴ dx = dt\)
\(⇒ ∫\frac {1}{\sqrt {x^2+2x+2}} dx = ∫\frac {1}{\sqrt {t^2+1}} dt\)
\(=log\ |t+\sqrt {t^2+1}|+C\)
\(=log\ |(x+1)+\sqrt {(x+1)^2+1}|+C\)
\(=log\ |(x+1)+\sqrt {x^2+2x+2}|+C\)
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There are many important integration formulas which are applied to integrate many other standard integrals. In this article, we will take a look at the integrals of these particular functions and see how they are used in several other standard integrals.
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- ∫1/(x2 – a2) dx = (1/2a) log|(x – a)/(x + a)| + C
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These are tabulated below along with the meaning of each part.
