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int(dx)/(x^2+2x+2)equals(A) xtan^(-1)(x+...

`int(dx)/(x^2+2x+2)`equals(A) `xtan^(-1)(x+1)+C` (B) `tan^(-1)(x+1)+C`(C) `(x+1)tan^(-1)x+C` (D) `tan^(-1)x+C`

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To solve the integral \(\int \frac{dx}{x^2 + 2x + 2}\), we will follow these steps: ### Step 1: Simplify the Denominator First, we need to rewrite the quadratic expression in the denominator in a more manageable form. We can complete the square for the expression \(x^2 + 2x + 2\). \[ x^2 + 2x + 2 = (x^2 + 2x + 1) + 1 = (x + 1)^2 + 1 \] ...
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