∫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 -
经济数学团队为你解答，满意请采纳！
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