∫e的负x次方乘以sin2xdx的不定积分是什么,
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![∫e的负x次方乘以sin2xdx的不定积分是什么,](/uploads/image/z/3014267-59-7.jpg?t=%E2%88%ABe%E7%9A%84%E8%B4%9Fx%E6%AC%A1%E6%96%B9%E4%B9%98%E4%BB%A5sin2xdx%E7%9A%84%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%E6%98%AF%E4%BB%80%E4%B9%88%2C)
∫e的负x次方乘以sin2xdx的不定积分是什么,
∫e的负x次方乘以sin2xdx的不定积分是什么,
∫e的负x次方乘以sin2xdx的不定积分是什么,
∫e^-x *sin2xdx
=-∫e^-x *sin2xd(-x)
=-∫sin2xde^-x
=-e^-xsin2x+∫e^-x*cos2x*2dx
=-e^-xsin2x-2∫e^-x*cos2xd(-x)
=-e^-xsin2x-2∫cos2xde^-x
=-e^-xsin2x-2e^-xcos2x+2∫e^-x*(-sin2x)*2dx
=-e^-xsin2x-2e^-xcos2x-4∫e^-x*sin2xdx
∴5∫e^-x *sin2xdx=-e^-xsin2x-2e^-xcos2x
∫e^-x *sin2xdx=-e^-x *(sin2x+2cos2x )/5
令A=∫ e^(-x)sin2xdx
∵A=∫ e^(-x)sin2xdx = - ∫ sin2xd(e^(-x))=-e^(-x)sin2x+∫ e^(-x)d(sin2x)
=-e^(-x)sin2x+2∫ e^(-x)cos2xdx
=-e^(-x)sin2x-2∫ cos2xd(e^(-x))
=-e^(-x)sin2x-2cos2x*e^(-x...
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令A=∫ e^(-x)sin2xdx
∵A=∫ e^(-x)sin2xdx = - ∫ sin2xd(e^(-x))=-e^(-x)sin2x+∫ e^(-x)d(sin2x)
=-e^(-x)sin2x+2∫ e^(-x)cos2xdx
=-e^(-x)sin2x-2∫ cos2xd(e^(-x))
=-e^(-x)sin2x-2cos2x*e^(-x)+2∫ e^(-x)d(cos2x)
=-e^(-x)sin2x-2cos2x*e^(-x)-4∫ e^(-x)sin2xdx
=-e^(-x)sin2x-2cos2x*e^(-x)-4A
5A=-e^(-x)sin2x-2cos2x*e^(-x)
∴A=∫ e^(-x)sin2xdx
=1/5[-e^(-x)sin2x-2cos2x*e^(-x)]+C
=-1/5(sin2x+2cos2x)e^(-x) +C
收起
用分步积分
I=∫e^(-x)sin2xdx
=-∫e^(-x)sin2xd(-x)
=-∫sin2xde^(-x)
=-e^(-x)sin2x+∫e^(-x)dsin2x
=-e^(-x)sin2x+2∫e^(-x)cos2xdx
=-e^(-x)sin2x-2∫cos2xde^(-x)
=-e^(-x)sin2x-2e^(-x)cos2x...
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用分步积分
I=∫e^(-x)sin2xdx
=-∫e^(-x)sin2xd(-x)
=-∫sin2xde^(-x)
=-e^(-x)sin2x+∫e^(-x)dsin2x
=-e^(-x)sin2x+2∫e^(-x)cos2xdx
=-e^(-x)sin2x-2∫cos2xde^(-x)
=-e^(-x)sin2x-2e^(-x)cos2x+2∫e^(-x)dcos2x
=-e^(-x)sin2x-2e^(-x)cos2x-4∫e^(-x)sin2xdx
移项得
I=∫e^(-x)sin2xdx=1/5[-e^(-x)sin2x-2e^(-x)cos2x]+C
收起