求不定积分∫2xarctanxdx
求不定积分∫2xarctanxdx -
=x^2.arctanx -∫x^2/(1+x^2) dx =x^2.arctanx -∫[1 - 1/(1+x^2)] dx =x^2.arctanx -x +arctanx + C
分部积分,方法如下,请作参考:
=x^2.arctanx -∫x^2/(1+x^2) dx =x^2.arctanx -∫[1 - 1/(1+x^2)] dx =x^2.arctanx -x +arctanx + C
分部积分,方法如下,请作参考:
方法如下,请作参考:若有帮助,请采纳。
∫2xarctanxdx=∫arctanxd(x^2)=x^2*arctanx-∫x^2darctanx =x^2*arctanx-∫(1-1/1+x^2)dx =x^2*arctanx-x+arctanx+C 两部分相加得所求积分为xarctanx-ln(1+x^2)/2+x^2*arctanx-x+arctanx+C
求不定积分∫x^2arctanxdx怎么求? -
∫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到此结束了?。
先用凑微分法,然后分部积分,再又凑微分法,详细如下图片:
不定积分∫arctanxdx怎样求解? -
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^3arctanx-1/6x^2+1/6ln(1+x^2)+C(C为常数)设函数和u,v具有连续导数,则d(uv)=udv+vdu。移项得到udv=d(uv)-vdu 。两边积分,得分部积分公式∫udv=uv-∫vdu。
∫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等会说。
求不定积分∫x^2arctanxdx -
∫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等我继续说。
= (1/2)x^2(arctanx) - (1/2)∫ dx+ (1/2)∫ 1/(1+x^2) dx = (1/2)x^2(arctanx) - (1/2)x + (1/2) arctanx + C 不定积分释义:微积分的重要概念。如果在区间i内,f′=f,那么函数f就称为f在区间i内的原函数。原函数的一般表达式f+c(c是任一常数)称为f的说完了。