3/ P=e∫11+x2lnxx+x2lnxdx
=e∫1x+x2lnx−x+1x+x2lnxdx
=e∫1(1−x−1x+x2lnx)dx
=e∫1(1−x+xlnx−1−xlnxx(1+xlnx))dx
$= \int\limits_1^e {\left( {1 - \frac{{x + x\ln x}}{{1 +
xlnx}} + \frac{1}{x}} \right)} dx= e + 1 - \int\limits_1^e {\frac{{x + x\ln x}}{{1 +
xlnx}}dx} Tớiđâyđặtt = 1 + x\ln x$ là xong.
3/
P=e∫11+x2lnxx+x2lnxdx
=e∫1x+x2lnx−x+1x+x2lnxdx
=e∫1(1−x−1x+x2lnx)dx
=e∫1(1−x+xlnx−1−xlnxx(1+xlnx))dx
$= \int\limits_1^e {\left( {1 - \frac{{
1 + \ln x}}{{1 +
xlnx}} + \frac{1}{x}} \right)} dx
= e + 1 - \int\limits_1^e {\frac{{
1 + \ln x}}{{1 +
xlnx}}dx}
Tớiđâyđặtt = 1 + x\ln x$ là xong.