What is the integral of 2arctan(5y) ?

The integral of 2arctan(5y) is 2(yarctan(5y)-1/10 ln|25y^2+1|)+C

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integral of 2arctan(5y)

\int 2 arctan (5 y) d y

2 (y arctan (5 y) - \frac{1}{10} ln 25 y^{2} + 1) + C

Solution steps

\int 2 arctan (5 y) d y

Take the constant out:

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

= 2 \cdot \int arctan (5 y) d y

Apply Integration By Parts

: y arctan (5 y) - \int \frac{5 y}{25 y ^{2} + 1} d y

= 2 (y arctan (5 y) - \int \frac{5 y}{25 y ^{2} + 1} d y)

\int \frac{5 y}{25 y ^{2} + 1} d y = \frac{1}{10} ln 25 y^{2} + 1

= 2 (y arctan (5 y) - \frac{1}{10} ln 25 y^{2} + 1)

Add a constant to the solution

= 2 (y arctan (5 y) - \frac{1}{10} ln 25 y^{2} + 1) + C

x \to 0 lim (sin (5 x))

\frac{d}{d x} (\frac{( x + 1 ) ( x - 2 )}{( x - 1 ) ( x + 2 )})

f (x) = e^{x - 1} - 1

y^{^{'}} - 3 y = \frac{y}{x}

\int 6 x^{2} - 4 x d x

What is the integral of 2arctan(5y) ?
The integral of 2arctan(5y) is 2(yarctan(5y)-1/10 ln|25y^2+1|)+C