∫x*arctan2xdx
∫x*arctan2xdx -
=xarctan2x-∫x*2/(1+4x^2)dx =xarctan2x-∫1/4*d(1+4x^2)/(1+4x^2)=xarctan2x-1/4*ln(1+4x^2)+C
=xarctan2x-∫x*2/(1+4x^2)dx =xarctan2x-∫1/4*d(1+4x^2)/(1+4x^2)=xarctan2x-1/4*ln(1+4x^2)+C
=xarctan2x-∫x*2/(1+4x^2)dx =xarctan2x-∫1/4*d(1+4x^2)/(1+4x^2)=xarctan2x-1/4*ln(1+4x^2)+C
=xarctan2x-∫x*2/(1+4x^2)dx =xarctan2x-∫1/4*d(1+4x^2)/(1+4x^2)=xarctan2x-1/4*ln(1+4x^2)+C
∫arctan2xdx=x*arctan2x-∫x darctan2x =x arctan2x-∫2x/(1+4x^2)dx =x arctan2x-1/4∫1/(1+4x^2)d(1+4x^2) x arctan2x-1/4 ln(1+4x^2)+c。在微积分中,一个函数f 的不定积分,或原函数,或反导数,是一个导数等于f 的函数F ,即F ′ = f。不定积分和定积分好了吧!
∫xarctan2xdx =(1/2)∫arctan2xd(x²)=(1/2)[x²*arctan2x-∫x²d(arctan2x)]=(1/2)x²*arctan2x-(1/2)*∫x²[1/(1+4x²)]*2dx =(1/2)x²*arctan2x-∫[x²/(1+4x²)]dx =(1/2)x²*arctan2x-(1/4)∫到此结束了?。
x乘以arctan2x的不定积分 -
∫xarctan2xdx = (1/2)∫arctan2xdx^2 = (1/2)x^2arctan2x - (1/2)∫2x^2/(1+4x^2)dx = (1/2)x^2arctan2x - (1/4)∫(1+4x^2-1)/(1+4x^2)dx = (1/2)x^2arctan2x - x/4 +(1/8)∫1/(1+4x^2)d(2x)= (1/2)x^2arctan2x - x/4 +(1/8)arctan后面会介绍。
∫arctan2xdx=x*arctan2x-∫x darctan2x =x arctan2x-∫2x/(1+4x^2)dx =x arctan2x-1/4∫1/(1+4x^2)d(1+4x^2) x arctan2x-1/4 ln(1+4x^2)+c。在微积分中,一个函数f 的不定积分,或原函数,或反导数,是一个导数等于f 的函数F ,即F ′ = f。不定积分和定积分好了吧!
∫xarctan2xdx -
我这有个关于∫xarctanxdx =∫arctanxd(0.5*x^2)=0.5*x^2 arctanx-∫0.5*x^2d(arctanx)=0.5*x^2 arctanx-∫0.5*x^2/(1+x^2)dx =0.5*x^2 arctanx-0.5*∫(1-(1/(1+x^2))dx =0.5*x^2 arctanx-0.5*∫dx+0.5*∫(1/(1+x^2))dx =0.5*x^2 a到此结束了?。
【答案】:
xarctan2xdx求不定积分 -
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分部积分:∫arctan2xdx=xarctan2x-∫[2x/(1+4x²)dx=xarctanx-∫d(x²)(1+4x²) xarctan2x-0.25ln(1+4x²)C,代入上下限得结果为π/8-0.25ln2