What is the integral of 1/(12(x^2+1)) ?

The integral of 1/(12(x^2+1)) is 1/12 arctan(x)+C

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integral of 1/(12(x^2+1))

\int \frac{1}{12 ( x ^{2} + 1 )} d x

\frac{1}{12} arctan (x) + C

Solution steps

\int \frac{1}{12 ( x ^{2} + 1 )} d x

Take the constant out:

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

= \frac{1}{12} \cdot \int \frac{1}{x ^{2} + 1} d x

Use the common integral:

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

= \frac{1}{12} arctan (x)

Add a constant to the solution

= \frac{1}{12} arctan (x) + C

x \to 3 + lim (\frac{x}{x - 3})

(1 + x) y^{^{'}} - x y = x + x^{2}

\frac{\partial}{\partial y} (x^{2} e^{y^{2}})

\frac{d}{d x} (5 x^{3} 5 x - 2)

\int 1 - x^{2} + \frac{1}{2} x^{4} d x

What is the integral of 1/(12(x^2+1)) ?
The integral of 1/(12(x^2+1)) is 1/12 arctan(x)+C