(sinx + cosx) / (sin^4x +cos^4x)



(sinx+cosx)(1-2sin^2(x)cos^2(x))



sinx-cosx=t



=sin^2(x)+cos^2(x) -2sinxcosx=t^2



1-2sinxcosx=t^2



1-t^2=2sinxcosx



1+t^4-2t^2=4sin^2(x)cos^2(x)







(cosx+sinx)dx=dt



dt/(1/2+t^2-t^4/2)



 2dt/(-t^4+2t^2+1)

2dt/(2-(t^2-1)^2)

2dt/(root2-t^2+1)(root2+t^2-1)

dt[1/(root2-t^2+1)+1/(root2+t^2-1)]1/root2

simplify using the formula

1/a^2-x^2 =1/2alog[(a-x)/(a+x)]

if u have any doubt, plz nudge me