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

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

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

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

4 arctan (x) + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= 4 arctan (x)

Add a constant to the solution

= 4 arctan (x) + C

f (x) = (x - 3)^{2} - 2, at x = 0

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\frac{\partial}{\partial y} (y^{3} + x^{2} y - 3 y)

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