Consider the function .

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Consider the function

f(x)=2x\,(x^{2}+1)^{2}\,e^{\,(x^{2}+1)^{3}}

. (i) Evaluate the indefinite integral

\displaystyle \int f(x)\,dx

. Express your answer in its simplest form. (ii) Using the result of part (i), calculate the exact value of

\displaystyle \int_{0}^{1} f(x)\,dx

. Simplify your final answer.