What is the integral of x/((2+x^2)) ?

The integral of x/((2+x^2)) is 1/2 ln|2+x^2|+C

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integral of x/((2+x^2))

\int \frac{x}{( 2 + x ^{2} )} d x

\frac{1}{2} ln 2 + x^{2} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = 2 + x^{2}

= \frac{1}{2} ln 2 + x^{2}

Add a constant to the solution

= \frac{1}{2} ln 2 + x^{2} + C

x \to 1 lim ((1 + \frac{8}{- 1})^{- x})

d x = x x^{2} - 16 d y

\frac{6}{5 x + 2}

\int 3 y d y

\frac{\partial}{\partial y} (9 - x^{2} - y^{2})

What is the integral of x/((2+x^2)) ?
The integral of x/((2+x^2)) is 1/2 ln|2+x^2|+C