What is expand ((1+x^2)arctan(x)-x)/2 ?

The solution to expand ((1+x^2)arctan(x)-x)/2 is (arctan(x))/2+(x^2arctan(x))/2-x/2

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expand ((1+x^2)arctan(x)-x)/2

expand

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

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

Solution steps

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

Expand

(1 + x^{2}) arctan (x) - x : arctan (x) + x^{2} arctan (x) - x

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

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

(9 + 5 cos^{2} (0.4 x)) \cdot (5 e^{- 0.5 x} + 2 e^{0.15 x})

\frac{( x ^{4} + 3 ) ^{3}}{12}

- \frac{s}{( s + 1 ) ( s ^{2} - 2 s + 2 )}

2 (e^{s i n (\frac{x}{4})} - 1)

x (3 x + 5 vx) (v + x \frac{d v}{d x})

What is expand ((1+x^2)arctan(x)-x)/2 ?
The solution to expand ((1+x^2)arctan(x)-x)/2 is (arctan(x))/2+(x^2arctan(x))/2-x/2