x^2arctanxdx
x^2arctanxdx不定积分求过程 -
∫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还有呢?
=(x^+1)^2arctanx-[∫(x^2+1)x+∫2x(x^2+1)arctanxdx]移项后再积分得∫2x(x^2+1)arctanxdx=0.5(x^2+1)2arctanx-x^3/6-x/2+C
∫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还有呢?
=(x^+1)^2arctanx-[∫(x^2+1)x+∫2x(x^2+1)arctanxdx]移项后再积分得∫2x(x^2+1)arctanxdx=0.5(x^2+1)2arctanx-x^3/6-x/2+C
∫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。
-
猜你感兴趣:
x2arctanxdx的定积分0到1