What is the integral of arctan(y) ?

The integral of arctan(y) is yarctan(y)-1/2 ln|y^2+1|+C

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integral of arctan(y)

\int arctan (y) d y

y arctan (y) - \frac{1}{2} ln y^{2} + 1 + C

Solution steps

\int arctan (y) d y

Apply Integration By Parts

: y arctan (y) - \int \frac{y}{y ^{2} + 1} d y

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

\int \frac{y}{y ^{2} + 1} d y = \frac{1}{2} ln y^{2} + 1

= y arctan (y) - \frac{1}{2} ln y^{2} + 1

Add a constant to the solution

= y arctan (y) - \frac{1}{2} ln y^{2} + 1 + C

f (x) = x^{4} + 5 e^{x}, (0, 5)

cos^{2} (x) sin (x) (\frac{d y}{d x}) + (cos^{3} (x)) y = 1

x \to 0 lim (x^{n} \cdot cos (\frac{3}{x}))

\int \frac{4 - 9 x}{x} d x

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

What is the integral of arctan(y) ?
The integral of arctan(y) is yarctan(y)-1/2 ln|y^2+1|+C