Define . What is the coefficient of in the Maclaurin series for…

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

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}

(b)

\dfrac{1}{5}

(c)

-\dfrac{1}{3}

(d)

\dfrac{1}{3}