`secx=2`

secx = - sqrt(2) .

The principal solution secx=sqrt(2) are

General solution of secx=sqrt(2) is

int_(0)^(pi//2)(secx)/(secx+cosecx)dx=

The integral int (sec^2x)/(secx+tanx)^(9/2)dx equals to (for some arbitrary constant K ) (A) -1/(secx+tanx)^(11/2){1/11-1/7(secx+tanx)^2}+K (B) 1/(secx+tanx)^(11/2){1/11-1/7(secx+tanx)^2}+K (C) -1/(secx+tanx)^(11/2){1/11+1/7(secx+tanx)^2}+K (D) 1/(secx+tanx)^(11/2){1/11+1/7(secx+tanx)^2}+K

The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitrary constant K)dot -1/((secx+tanx)^((11)/2)){1/(11)-1/7(secx+tanx)^2}+K 1/((secx+tanx)^(1/(11))){1/(11)-1/7(secx+tanx)^2}+K -1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K 1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K

The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitrary constant K)dot -1/((secx+tanx)^((11)/2)){1/(11)-1/7(secx+tanx)^2}+K 1/((secx+tanx)^(1/(11))){1/(11)-1/7(secx+tanx)^2}+K -1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K 1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K

The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitrary constant K)dot (a) -1/((secx+tanx)^((11)/2)){1/(11)-1/7(secx+tanx)^2}+K (b) 1/((secx+tanx)^(1/(11))){1/(11)-1/7(secx+tanx)^2}+K (c) -1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K (d) 1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K

The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitrary constant K)dot -1/((secx+tanx)^((11)/2)){1/(11)-1/7(secx+tanx)^2}+K 1/((secx+tanx)^(1/(11))){1/(11)-1/7(secx+tanx)^2}+K -1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K 1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K

The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitrary constant K)dot -1/((secx+tanx)^((11)/2)){1/(11)-1/7(secx+tanx)^2}+K 1/((secx+tanx)^(1/(11))){1/(11)-1/7(secx+tanx)^2}+K -1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K 1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K