What is the integral of t(arctan(t)) ?

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

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integral of t(arctan(t))

\int t (arctan (t)) d t

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

Solution steps

\int t arctan (t) d t

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{d}{d p} (3 p (1 - 0.5 p))

\frac{d}{d x} (\frac{- 6}{( x + 1 ) ^{4}})

\frac{\partial}{\partial x} (1 + \frac{c}{x} - \frac{b}{x ^{3}})

k = 1 \sum \infty ln (1 + \frac{1}{k})

x^{2} y^{^{'}} - x y = x^{- 7} y^{\frac{1}{2}}

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