求不定积分：∫ cos(ln x) dx

∫ cos(ln x) dx
= ∫ xcos(ln x) d(ln x)
= ∫ x d(sin(ln x))
= xsin(ln x) - ∫ sin(ln x) dx
= xsin(ln x) - ∫ xsin(ln x) d(ln x)
= xsin(ln x) + ∫ x d(cos(ln x))
= xsin(ln x) + xcos(ln x) - ∫ cos(ln x) dx
2∫ cos(ln x) dx= xsin(ln x) + xcos(ln x)
∫ cos(ln x) dx = (1/2)x[sin(ln x) + cos(ln x)]

令A=∫ cos ln x dx ，则：
A=∫ cos ln x dx
=x cos ln x - ∫ x d(cos ln x)
=x cos ln x + ∫ x sin ln x (1/x) dx
=x cos ln x + ∫ sin ln x dx
=x co...

霸王正解