What is the integral of 2yarctan(x) ?

The integral of 2yarctan(x) is y^2arctan(x)+C

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integral of 2yarctan(x)

\int 2 y arctan (x) d y

y^{2} arctan (x) + C

Solution steps

\int 2 y arctan (x) d y

Take the constant out:

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

= 2 arctan (x) \cdot \int y d y

Apply the Power Rule

: \frac{y ^{2}}{2}

= 2 arctan (x) \frac{y ^{2}}{2}

Simplify

2 arctan (x) \frac{y ^{2}}{2} : y^{2} arctan (x)

= y^{2} arctan (x)

Add a constant to the solution

= y^{2} arctan (x) + C

y^{^{''}} - 2 y^{^{'}} - 24 y = 0, y (0) = - 1, y^{^{'}} (0) = 14

\int \frac{( x ^{3} )}{( x ^{4} + 5 )} d x

\int \frac{6}{sec ( 2 x ) - 1} d x

\int (a - b y)^{4} d y

x \to 5 + lim (x^{2} + 2 x - 3)

What is the integral of 2yarctan(x) ?
The integral of 2yarctan(x) is y^2arctan(x)+C