求不定积分∫e^2x * cos e^x dx

∫e^2x * cos e^x dx
= ∫e^x * cos e^x d(e^x)
= ∫y*cosydy ___________________y = e^x
= ∫ydsiny
= y*siny - ∫sinydy
= y*siny +cosy + C
= e^x*sin(e^x) + cos(e^x) + C

令e^x=t,则d(e^x)=e^x*dx
∫e^2x * cos e^x dx
=∫e^x*e^x*cose^xdx
=∫tcostdt
=tsint+cost+C

所以∫e^2x * cos e^x dx=e^xsin(e^x)+cos(e^x)+C(其中C为常数)

令e^x=t,则d(e^x)=e^x*dx
∫e^2x * cos e^x dx
=∫e^x*e^x*cose^xdx
=∫tcostdt
=tsint+cost+C

所以∫e^2x * cos e^x dx=e^xsin(e^x)+cos(e^x)+C

高数上的。。