xlnxdx的不定积分讲解

莘顾俩2119求不定积分, 不定积分(根号x乘lnx )dx -
嵇轰昌19313827665 ______ ∫xlnxdx =0.5∫lnxdx2 =0.5x2lnx-0.5∫x2dlnx =0.5x2lnx-0.5∫xdx =0.5x2lnx-0.25x2+C

莘顾俩2119xln(x+根号1+x^2)的积分,用分部积分发,不定积分,最好说一下此类题的思路, -
嵇轰昌19313827665 ______[答案] ∫xln[x+√(1+x²)]dx =(1/2)∫ln[x+√(1+x²)]dx² =(1/2)(x²ln[x+√(1+x²)]-∫x²dln[x+√(1+x²)]) =(1/2)(x²ln[x+√(1+x²)]-∫x²/√(1+x²)dx) ∫x²/√(1+x²)dx用三角 令x=tanθ,则θ=arctanx ∫x²/√(1+x²)dx =∫sin²θ/cos³θdθ =-∫sinθ/cos³θdcosθ =(1/2)...

莘顾俩2119用分部积分法计算定积分,∫xlnxdx {∫上面为e,下面为1} -
嵇轰昌19313827665 ______[答案] ,∫(e,1)xlnxdx=1/2∫(e,1)lnxdx²=1/2*x²lnx(e,1)-1/2∫(e,1)x²dlnx=1/2*x²lnx(e,1)-1/2∫(e,1)x²*1/xdx=1/2*x²lnx(e,1)-1/2∫(e,1)xdx=[1/2*x²lnx-x²/4](e,1)=e²/2-e...

莘顾俩2119计算不定积分∫x^2lnxdx -
嵇轰昌19313827665 ______[答案] ∫ x^2 lnx dx =∫ lnx d(x^3/3) = (1/3)x^3 lnx - (1/3)∫ x^3 dlnx = (1/3)x^3 lnx - (1/3)∫ x^2 dx = (1/3)x^3 lnx - (1/3)(x^3/3) + C = (1/3)x^3 lnx - (1/9)x^3 + C = (1/9)(3lnx - 1)x^3 + C

莘顾俩2119计算不定积分:∫xlnxdx,用的分布积分uv'dx=uv - u'vdx吗?但是uv'dx的v'怎么出来的? -
嵇轰昌19313827665 ______[答案] u=lnx 令 v'=x 求v 其实也就是求x的原函数,即是求x的不定积分.

莘顾俩2119求下列不定积分1.∫xlnxdx2.∫xcos2xdx3.∫ln(1+x的平方)dx4.∫1+9x的平方分之一dx -
嵇轰昌19313827665 ______[答案] 1、∫xlnxdx =(1/2)∫lnxd(x^2)= (1/2)[x^2lnx-∫x^2d(lnx)]=(1/2)[x^2lnx-∫x^2*dx/x]=x^2[lnx-(1/2)+c]/22,∫xcos2xdx =(1/2)∫xdsin2x=(1/2)[xsin2x-∫sin2xdx=(1/2)[xsin2x+ (1/2) ∫dcos2x=(1/2)[xsin2x+(1/2)c...

莘顾俩2119求下列不定积分或定积分 1,∫(x^4+cosx)dx 2,∫cosxsin^3xdx 3,∫xlnxdx 4,∫|x - 3|dx求下列不定积分或定积分 1,∫(x^4+cosx)dx 2,∫cosxsin^3xdx 3,∫xlnxdx 4,∫|x - 3|dx -
嵇轰昌19313827665 ______[答案] 1、 ∫(x^4+cosx) dx = (1/5)x^5+sinx + C 2、 ∫(cosxsin³x) dx = ∫sin³x d(sinx) = (1/4)sin^4x + C 3、 ∫xlnx dx = ∫lnx d(x²/2) = (1/2)x²lnx - (1/2)∫x²*1/x dx = (1/2)x²lnx - (1/2)∫x dx = (1/2)x²lnx - (1/4)x² + C 4、 |x-3|=[√(x-3)]² =-(x-3)=-x+3 for x= x-3 for ...

莘顾俩2119∫xlnxdx 怎么算 -
嵇轰昌19313827665 ______[答案] 用分部积分法 ∫xlnxdx =∫lnx d1/2x^2 =1/2x^2 *lnx -∫1/2x^2 dlnx =1/2x^2 *lnx -∫1/2x dx =1/2x^2 *lnx -1/4x^2 =1/2x^2*(lnx -1/2) + C(常数)