x^2arctanxdx

x^2arctanxdx

∫x^2arctanxdx的积分公式是什么? -
∫x^2arctanxdx=1/3x^3arctanx-1/6x^2+1/6ln(1+x^2)+C。（C为积分常数）∫(x^2)*arctanxdx =1/3∫arctanxdx^3 =1/3x^3arctanx-1/3∫x^3/(1+x^2)dx =1/3x^3arctanx-1/6∫x^2/(1+x^2)dx^2 =1/3x^3arctanx-1/6∫[1-1/(1+x^2)]dx^2 =1/3x^3arc希望你能满意。
原式=arctanx*x^3/3-∫x^3/3d(arctanx)=arctanx*x^3/3-(1/3)∫(x^3/(x^2+1))dx =arctanx*x^3/3-(1/3)∫(x-x/(x^2+1))dx =arctanx*x^3/3-(1/3)∫xdx+(1/6)∫d(x^2+1)/(x^2+1)=arctanx*x^3/3-x^2/6+(1/6)ln|x^2+1|+C 有帮助请点赞。
∫x^2arctanxdx的不定积分怎么积 -
方法如下，请作参考：若有帮助，请采纳。
∫x^2arctanxdx=1/3x^3arctanx-1/6x^2+1/6ln(1+x^2)+C。（C为积分常数）∫(x^2)*arctanxdx =1/3∫arctanxdx^3 =1/3x^3arctanx-1/3∫x^3/(1+x^2)dx =1/3x^3arctanx-1/6∫x^2/(1+x^2)dx^2 =1/3x^3arctanx-1/6∫[1-1/(1+x^2)]dx^2 =1/3x^3arc希望你能满意。
∫x²arctanxdx怎么算 -
∫x^2arctanxdx=(1/3)∫arctanxdx^3 =(1/3)x^3arctanx-(1/3)∫x^3darctanx =(1/3)x^3arctanx-(1/3)∫[(x^3+x)-x]/(1+x^2)dx =(1/3)x^3arctanx-(1/3)∫xdx+(1/3)∫(x)/(1+x^2)dx =(1/3)x^3arctanx-(1/6)x^2+(1/6)ln(1+x^2)+C（C为还有呢？
=x³/3arctanx-∫x³/3·1/(1+x²)dx =x³/3arctanx-1/3∫(x³+x-x)/（1+x²）dx =x³/3artanx-1/3∫[x-x/(1+x²)]dx =x³/3artanx-x²/6+1/6∫1/(1+x²)d(1+x²)=x³/3arctanx-x&还有呢？
求不定积分:x^2·arctanx -
解：∫x²arctanxdx=∫arctanxd(x³/3)=(x³arctanx)/3-1/3∫x³dx/(1+x²) (应用分部积分法)=(x³arctanx)/3-1/6∫(1+x²-1)d(x²)/(1+x²)=(x³arctanx)/3-1/6∫(1-1/(1+x²))d(x²)=(到此结束了？。
对于第三项，令u=1+x²,du=2xdx,∴dx=(1/2x)du =(1/3)x³arctan(x)-(1/3)(x²/2)+(1/3·1/2)∫1/u du =(1/3)x³arctan(x)-(1/6)x²+(1/6)ln|u|+C =(1/3)x³arctan(x)-(1/6)x²+(1/6)ln|1+x²|+C 有帮助请点赞。

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