2道积分题目1).∫xcosx^2dx2)∫tan^3xsecxdx

Question

2道积分题目
1).∫xcosx^2dx 2)∫tan^3xsecxdx

Answer 1

=∫x(cos2x+1)/2 dx
=1/4∫xcos2xd2x+∫x/2dx
=1/4∫xdsin2x+x²
=1/4xsin2x-1/4∫si2xdx+x²
=1/4xsin2x+1/8cos2x+x²+C
=∫tan²xdsecx
=∫(sec²x-1)dsecx
=sec³x/3-secx+C