What is the integral of 1/(4(x^2+1)) ?

The integral of 1/(4(x^2+1)) is 1/4 arctan(x)+C

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integral of 1/(4(x^2+1))

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

\frac{1}{4} arctan (x) + C

Solution steps

\int \frac{1}{4 ( 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}{4} \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}{4} arctan (x)

Add a constant to the solution

= \frac{1}{4} arctan (x) + C

\int cos (x) - 5 sin (x) d x

\frac{d}{d x} (7 x + 3)

\frac{d}{d x} (x^{x^{4}})

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

y^{^{''}} = x

What is the integral of 1/(4(x^2+1)) ?
The integral of 1/(4(x^2+1)) is 1/4 arctan(x)+C