Work out the following two integrals

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

Problem

Work out the following two integrals, using the result of the first to assist with the second wherever appropriate. (a) Evaluate

I_{1}=\displaystyle\int x\,\ln x\,dx

. (b) Hence or otherwise, determine

I_{2}=\displaystyle\int (\ln x)^{2}\,dx