What is the integral of 5xarctan(x) ?

The integral of 5xarctan(x) is 5(1/2 x^2arctan(x)-1/2 (-arctan(x)+x))+C

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integral of 5xarctan(x)

\int 5 x arctan (x) d x

5 (\frac{1}{2} x^{2} arctan (x) - \frac{1}{2} (- arctan (x) + x)) + C

Solution steps

\int 5 x arctan (x) d x

Take the constant out:

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

= 5 \cdot \int x arctan (x) d x

Apply Integration By Parts

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

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

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

= 5 (\frac{1}{2} x^{2} arctan (x) - \frac{1}{2} (- arctan (x) + x))

Add a constant to the solution

= 5 (\frac{1}{2} x^{2} arctan (x) - \frac{1}{2} (- arctan (x) + x)) + C

\frac{\partial}{\partial y} ((e^{x} - 4 x) cos (y))

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

\frac{d}{d x} (ln ((x - 1)^{3} (x^{2} + 1)^{4}))

\frac{d}{d x} (3 x^{2} - e^{2 x})

\frac{d y}{d t} = - \frac{3 y}{t} - 2 - t^{- 4}

What is the integral of 5xarctan(x) ?
The integral of 5xarctan(x) is 5(1/2 x^2arctan(x)-1/2 (-arctan(x)+x))+C