不定积分∫dx/[sin(x+3)cos(x+3)]计算步骤

=ln|tan(x+3)|+C

两种方法求函数y=(2sin2x+1)^(cos2x)的导数

∵y=(2sin2x+1)^(cos2x)∴lny=cos2x*ln(2sin2x+1),两边同时对x求导,则:dy/y=-sin2x*ln(2sin2x+1)dx+2cos2x*cos2xdx/(2sin2x+1)=[2cos2x*cos2x-sin2x*(2sin2x+1)*ln(2sin2x+1)]dx/(2sin2x+1),即:dy/dx=(2sin2x+1)^(cos2x)*[2cos2x*cos2x-sin2x*(2sin2x+1)*l...

学习如何求函数y=ln[(1+x)/(2-x)]的单调和凸凹区间

∴d^2y/d^2x=-3*[(2-x)+(x+1)*(-1)]/[(x+1)(2-x)]^2=3(2x-1)/[(x+1)(2-x)]^2。令d^2y/d^2x=0,则:2x-1=0,得x=1/2。(1).当x∈[1/2,2)时,d^2y/d^2x>0,则函数为凹函数,该区间为凹区间。(2).当x∈(-1,1/2)时,d^2y/d^2x<0,则函数为凸函数,...

函数88y=ln(x^2-9y^2)导数如何计算

dy/dx=x/[44(x^2+9y^2)+9y].构造函数导数法设F(x,y)=88y-ln(x^2-9y^2),则F(x,y)对x求导有:F'x=-2x/(x^2-9y^2),进一步F(x,y)对y求导有:F'y=88+18y/(x^2-9y^2),所以有:dy/dx=-F'x/F'y=[2x/(x^2-9y^2)]/[88+18y/(1x^2-9y^2)]=x/[44...

不定积分的求法-不定积分常用方法小结

=2∫d(tan2x)(tan2x)2+4=arctan(tan2x2)+c=2\int_{}^{}\frac{d(tan2x)}{(tan2x)^{2}+4}=arctan(\frac{tan2x}{2})+c得到式(1)(1)后,本题便容易求解了4.3I=∫x+1+lnx(x+1)2+(xlnx)2dx4.3I=\int_{}^{}\frac{x+1+lnx}{(x+1)^{2}+(xlnx)^{2}}dx...