Question

高数之微积分

求∫cos(lnx) dx.需要详解！

Answer 1

∫cos(lnx)dx
= xcos(lnx) + ∫{[xsin(lnx)]/x}dx
= xcos(lnx) + ∫sin(lnx)dx + c
= xcos(lnx) + xsin(lnx) - ∫{[xcos(lnx)]/x}dx + C
= xcos(lnx) + xsin(lnx) - ∫cos(lnx)dx + c
= x[cos(lnx) + sin(lnx)]/2 + c

Answer 2

答案:
x[cos(lnx) + sin(lnx)]/2 + c