Mathematics

Problem

Define

h(x)=x^{2}\displaystyle\int_{0}^{x}\frac{1}{1+t^{2}}\,dt

. What is the coefficient of

x^{5}

in the Maclaurin series for

h(x)

? a)

-\dfrac{1}{5}

\dfrac{1}{5}

-\dfrac{1}{3}

\dfrac{1}{3}