hello, referring me to sinusoidal functions i write: (qos(x))^4+(qin(x))^4=1;(qosh(x))^4-(qinh(x))^4=1; compound functions: qan(x)=qin(x)/qos(x); cqn(x)=qos(x)/qin(x); qanh(x)=qinh(x)/qosh(x); cqnh(x)=qosh(x)/qinh(x); derivates diff(qos(x),x)=-(qin(x))^3; diff(qin(x),x)=(qos(x))^3; diff(qosh(x),x)=(qinh(x))^3; diff(qinh(x),x)=(qosh(x))^3; diff(qan(x),x)=1/(qos(x))^2; diff(cqn(x),x)=-1/(qin(x))^2; diff(qanh(x),x)=1/(qos(x))^2; diff(cqnh(x),x)=-1/(qin(x))^2; reciprocal functions: aqos(x)=-integrate(1/(1-x^4)^(3/4), x); aqin(x)=integrate(1/(1-x^4)^(3/4), x); aqosh(x)=integrate(1/(x^4-1)^(3/4), x); aqinh(x)=integrate(1/(1+x^4)^(3/4), x); aqan(x)=integrate(1/(x^4+1)^(1/2), x); acqn(x)=-integrate(1/(1+x^4)^(1/2), x); a constancy noted sigma sigma=(Gamma(1/4))^2/(2*sqrt(Pi)); some special points. qos(0)=1 ; qin(0)=0 ; qos(sigma/2)=0; qin(sigma/2)=1; qos(sigma)=-1; qin(sigma)=0; qos(sigma/4)=1/2^(1/4); qin(sigma/4)=1/2^(1/4); qan(sigma/4)=1; some integrals integrate(1/sqrt(x^4+1), x= 0.. 1)=sigma/4; integrate(1/(1-x^4)^(3/4),x=0..1/2^(1/4))=sigma/4; integrate(1/(1-x^4)^(3/4),x=0..1)=sigma/2; integrate(1/(1-x^4)^(3/4),x=-1..1)=sigma; FME...