=∫ x(1+cos2x/2)dx
=1/2∫ xdx+1/2∫xcos2xdx
=x²/4+1/4∫xdsin2x
=x²/4+1/4*xsin2x-1/4∫sin2xdx
=x²/4+1/4*xsin2x-1/8∫sin2xd2x
=x²/4+1/4*xsin2x+1/8*cos2x+C
不定积分 :∫ xcos^2xdx 求详细过程和答案 拜托大神.
∫ xcos^2xdx =∫ x(1+cos2x\/2)dx =1\/2∫ xdx+1\/2∫xcos2xdx =x²\/4+1\/4∫xdsin2x =x²\/4+1\/4*xsin2x-1\/4∫sin2xdx =x²\/4+1\/4*xsin2x-1\/8∫sin2xd2x =x²\/4+1\/4*xsin2x+1\/8*cos2x+C ...
xcos^2x的不定积分
本题是不定积分基本练习题，具体步骤如下:∫ⅹcos^2xdx =∫x(1+cos2x)dx\/2 =(1\/2)∫xdx+(1\/2)∫xcos2xdx =(1\/2)*(1\/2)*x^2+(1\/4)∫ⅹcos2xd2x =(1\/2)*(1\/2)*x^2+(1\/4)∫ⅹdsin2x =(1\/4)ⅹ^2+(1\/4)ⅹsin2x-(1\/4)∫sin2xdx =(1\/4)ⅹ^2+(1\/4)ⅹs...
求不定积分∫x(cosx)^2dx
∫x(cosx)^2dx=∫xcos^2xdx =∫x(1+cos2x\/2)dx =1\/4x^2+1\/2∫xcos2xdx =1\/4x^2+1\/4∫xd(sin2x)=1\/4x^2+1\/4xsin2x-1\/4∫sin2xdx =1\/4x^2+1\/4xsin2x+1\/8cos2x+C 说明：C是常数 不可积函数 虽然很多函数都可通过如上的各种手段计算其不定积分，但这并不意味着所有...
求x*cos^2x的不定积分
∫x cos2x dx =1\/2∫x (1+cos2x)dx =1\/2∫xdx + 1\/4∫xdsin2x =x2\/4 + 1\/4 x sin2x - 1\/4∫sin2xdx =x2\/4 + 1\/4 x sin2x + 1\/8 cos2x + C 这个不是分步积分法！！是一般的化解法，先三角降次，再用凑微分法。楼上不要误导哦 ...
求∫xcos^2xdx等于多少,上限是2π,下限是0.谢谢!!
∫(0→2π) xcos²x dx = ∫(0→2π) x • (1 + cos2x)\/2 dx = (1\/2)∫(0→2π) x dx + (1\/2)∫(0→2π) xcos2x dx = (1\/4)[ x² ]：(0→2π) + (1\/4)∫(0→2π) x d(sin2x)= (1\/4)(4π²) + (1\/4)xsin2x：(0→2π...
求不定积分∫x^2cos^2xdx
倍角加分步 cos^2x=(cos2x+1)\/2 原因为化为 ∫1\/2*x^2dx+1\/4∫x^2dsin2x =1\/6x^3+1\/4sin2x*x^2-1\/2∫xsin2xdx =1\/6x^3+1\/4sin2x*x^2+1\/4xcos2x-1\/4∫cos2xdx =1\/6x^3+1\/4sin2x*x^2+1\/4xcos2x+1\/8sin2x 思路是这样,错没错不晓得 ...
cos^2x求不定积分
∫cos^2xdx =∫（1+cos2x）dx\/2 =∫(1+cos2x)d2x\/4 =(1\/4)∫[d2x+cos2xd2x]=(1\/4){2x+sin2x+C1} =x\/2+(sin2x)\/4+C 不定积分的公式 1、∫ a dx = ax + C，a和C都是常数 2、∫ x^a dx = [x^(a + 1)]\/(a + 1) + C，其中a为常数且 a ≠ -1 3、∫ 1...
求不定积分∫cos^2xdx
∫cos^2xdx =1\/2∫1+cos2xdx =1\/2(x+∫cos2xdx)=1\/2(x+1\/2∫dsin2x)=x\/2+sin2x\/4+C
求助:∫x^2cos^2xdx
解：原式=∫x²(1+cos(2x))\/2dx =x³\/6+1\/2∫x²cos(2x)dx =x³\/6+x²sin(2x)\/4-1\/2∫xsin(2x)dx (应用分部积分法)=x³\/6+x²sin(2x)\/4+xcos(2x)\/4-1\/4∫cos(2x)dx (应用分部积分法)=x³\/6+x²sin(2x)\/4+x...
cos^2X原函数是什么
cos^2x的原函数为1\/2x+1\/4sin2x+C 解：令F(x)为cos^2x的原函数。那么 F(x)=∫cos^2xdx =∫(cos2x+1)\/2dx =1\/2∫cos2xdx+1\/2∫1dx =1\/4∫cos2xd(2x)+1\/2∫1dx =1\/2x+1\/4sin2x+C
