∫cos(2-3x)dx

cos(x^2)dx1/3*-sin(x^3)微分啊，这个微分很简单的，一元函数的微分和导数是一样的，只是在后面加个dx,前面的函数是复合函数，先对cos()求导，在对里面的那部分求导，得出-sin(x^2)x2x=-2xsin(x^2)后

∫e^(2x)cos(3x)dx∫e^(2x)cos3xdx=(1/3)∫e^(2x)d(sin3x)=(1/3)e^(2x)sin3x-(1/3)∫sin3xde^(2x)=(1/3)e^(2x)sin3x-(2/3)∫e^(2x)sin

∫(cos^3x/sin^2x)dx∫(cos^3x/sin^2x)dx=∫[(1-(sinx)^2]/(sinx)^2dsinx=∫[1/(sinx)^2-1]dsinx=-1/sinx-sinx+C∫(cos^3x/sin^2x)dx=

∫[cos^3(x)]/[sin^2(x)]dx∫[cos^3(x)]/[sin^2(x)]dx=积分:(cos^2x)/(sin^2x)dsinx=积分:(1-sin^2x)/sin^2x)dsinx=积分;1/sin^2xdsin^2x

∫sin^3(x)cos^2(x)dx=把一个sin(x)拿出来∫sin^3(x)cos^2(x)dx=-∫sin^2(x)cos^2(x)d(cos(x))=-∫(1-cos^2)cos^2(x)d(cos(x))=-∫cos^2-cos

求积分：∫sin^2(x)/cos^3(x)dx原式等于：∫[1-cos^2(x)]/cos^3(x)dx=∫dx/cos^3(x)-∫dx/cos(x)=(secxtanx+ln|secx+tanx|)/2-ln|secx+tanx|+C

不定积分∫x*cos(x/3)*dx分部积分法∫udv=uv-∫vduu=3x,v=sin(x/3)结果是3xsin(x/3)+9cos(x/3)分部积分，，cos拿到d后面，，答案：3xsin(x/3)+9cos(x/3)+C。

∫x*(cos^2x)dx分步积分吧∫x*(cos^2x)dx=1/2∫x*(1+cos2x)dx=1/4x^2+1/2∫x*cos2xdx=1/4x^2+1/4∫x*dsin2x=1/4x^2+1/4x*sin2x-1/4∫sin2xdx

∫x／[(cos^2)x]dx∫x／[(cos^2)x]dx=∫xdtanx=xtanx-∫tanxdx（分部积分法）=xtanx+ln|cosx|+C

∫sin(x)cos^2(x)dx原式=-∫cos²xdcosx=-cos³x/3+C

∫cos(x-1)dx、∫x^3e^x^2dx怎么解∫cos(x-1)dx=∫cos(x-1)d(x-1)=sin(x-1)+C∫x³e^(x²)dx-->令u=x²,du=2xdx-->=∫uxe^u·du/

∫cos^3xdx∫tan^3xsecxdx∫(cosx)^3dx=∫(1-sinx^2)dsinx=sinx-(1/3)(sinx)^3+C∫tanx^3secxdx=∫tanx^2dsecx=∫(secx^2-1)dsecx=(1/3)

用换元法计算不定积分∫cos(3x+2)dx令t=3x+2,则dt=3dx→dx=1/3·dt∫cos(3x+2)dx=∫cost·1/3·dt=1/3·∫costdt=1/3·sint+C=1/3·sin(3x+2)+C

求∫cos(-2x+3)dx的不定积分

∫cos^2(x/2)dxcos(2x)=2cos^2(x)-1cos^2(x)=[1+cos(2x)]/2同理cos^2(x/2)=[1+cos(x)]/2∫cos^2(x/2)dx=∫[1+cos(x)]/2dx=∫1/2dx+∫cos

求∫2/(2+cosx)dx令t=tan(x/2)则cosx=[cos²(x/2)-sin²(x/2)]/[cos²(x/2)+sin²(x/2)]=[1-tan²(x/2)]/[1+tan

求:∫cos^2(2x)dxcos^2(2x）=2cos4x-1∫cos^2(2x)dx=∫（2cos4x-1）dx=1/4∫2cos4xd4x-∫dx=1/2sin4x-x+C(C为常数)

∫(1-cos^(2)2x)dx=∫(1-cos4x)/2dx=∫1/2dx-∫cos4x/8d4x=0.5x-1/8*sin4x+C(C为任意常数)

∫(2/cos^2x)dx=原式=2∫sec²xdx=2tanx+C

∫(sinx/cos^3x)dx∫(sinx/cos^3x)dx=-∫(dcosx/cos^3x)=1/2cos^2x