What is maclaurin (arctan(x))/(x+1) ?

The answer to maclaurin (arctan(x))/(x+1) is x-x^2+2/3 x^3-2/3 x^4+\ldots

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maclaurin (arctan(x))/(x+1)

maclaurin

\frac{arctan ( x )}{x + 1}

x - x^{2} + \frac{2}{3} x^{3} - \frac{2}{3} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( \frac{a r c t a n ( x )}{x + 1} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{a r c t a n ( x )}{x + 1} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{a r c t a n ( x )}{x + 1} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{4}{3 !} x^{3} + \frac{- 16}{4 !} x^{4} + \dots

Refine

= x - x^{2} + \frac{2}{3} x^{3} - \frac{2}{3} x^{4} + \dots

\frac{2}{( 1 + x ) ^{3}}

\frac{\partial}{\partial y} (y - cos (y))

\int_{0}^{1} \frac{8}{x ( 1 + x )} d x

f (x) = (x + 2)^{x}

x \to 2 lim (x^{2} + 3 x - 8)

What is maclaurin (arctan(x))/(x+1) ?
The answer to maclaurin (arctan(x))/(x+1) is x-x^2+2/3 x^3-2/3 x^4+\ldots