سیگما

`Q=int (dx)/(sinx+cosx)`
`t=tan(x/2)`
`sinx=(2t)/(1+t^2)`
`cosx=(1-t^2)/(1+t^2)`
`dx=(2dt)/(1+t^)`
`Q=int ((2)/(1+t^2))/((2t+1-t^2)/(1+t^2)) dt`
`Q=2 int (dt)/(2-(t-1)^2)`
`Q=sqrt(2)arctanh((tan(x/2)-1)/sqrt(2))`

`Q=int (cos^5x)/(sin^3x) dx`
`t=sinx`
`(dt)/(dx)=cosx`
`Q=int (cos^4x)/(sin^3x) cosx dx`
`Q=int sqrt(1-t^2)^4/t^3 dt`
`Q=int (t^4-2t^2+1)/t^3 dt`
`Q=int t-2/t+1/t^3 dt`
`Q=t^2/2-2lnt-1/(2t^2)`
`|t=sinx`

`Q=int (sin(x+pi/4))/(sinx cosx) dx`
`Q=int ((sinx+cosx)/sqrt(2))/(sinx cosx) dx`
`t=tan(x/2)`
`sinx=(2t)/(1+t^2)`
`cosx=(1-t^2)/(1+t^2)`
`dx=(2dt)/(1+t^)`
`Q=sqrt(2)/2 int ((2t+1-t^2)/(t^2+1))/((2t(1-t^2))/(1+t^2)^2) (2)/(1+t^2) dt`
`Q=sqrt(2) int (2t+1-t^2)/(2t-2t^3) dt`
`Q=int 1/(sqrt(2)t)-sqrt(2)/(t^2-1) dt`
`Q=sqrt(2)/2lnt-sqrt(2)arctanh(t)`

`Q=int (dx)/(sinhx+2coshx)`
`sinhx=(2t)/(1-t^2)`
`coshx=(1+t^2)/(1-t^2)`
`tanh(x/2)=t`
`dx=(2dt)/(1-t^2)`
`Q=int ((2)/(1-t^2))/((2t)/(1-t^2)+2(1+t^2)/(1-t^2)) dt`
`Q=int 1/(t^2+t+1) dt`
`Q=2/sqrt(3)arctan((2tanh(x/2)+1)/sqrt(3))`

`Q=int (dx)/(x root3(x^5+1))`
`t=x^5+1`
`(dx)/(dt)=1/5(t-1)^(-4/5)`
`Q=int (1/5(t-1)^(-4/5))/(root5(t-1)root3(t)) dt`
`Q=1/5 int (dt)/((t-1)root3(t))`
`u^3=t`
`(dt)/(du)=2u^2`
`Q=1/5 int (3u^2)/((u^3-1)u) du`
`Q=3/5 int u/(u^3-1) du`
`u/(u^3-1)=A/(u-1)+(Bx+C)/(u^2+u+1)`
`A=1/3,B=-1/3,C=1/3`
`Q=3/5(int (1/3)/(u-1)+(-1/3u+1/3)/(u^2+u+1) du)`
`Q=1/5(ln(u-1)-1/2(int (2u+1-3)/(u^2+u+1) du))`
`Q=1/10ln((u-1)^2/(u^2+u+1))+sqrt(3)/5arctan((2u+1)/sqrt(3))`
`|u=root3(1+x^5)`