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

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

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integral of 1/(1+r^2)

\int \frac{1}{1 + r ^{2}} d r

arctan (r) + C

Solution steps

\int \frac{1}{1 + r ^{2}} d r

Use the common integral:

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

= arctan (r)

Add a constant to the solution

= arctan (r) + C

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\frac{d}{d x} (π x^{2} h)

\int \frac{12}{x ( x ^{2} + 25 )} d x

csc^{2} (x) - 4

(x + 6 x y^{4}) d x + e^{x^{2}} y^{3} d y = 0