`int((2+secx)secx)/((1+2secx)^2)dx=`

sqrt(secx)

intdx/(1+secx)

int(dx)/(sinx+secx)

int(secx)/(1+c o s e c x)dx

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 value of lim_(xrarr2pi)(1-(secx)^(secx))/(ln(secx)) is equal to

intsecx(secx+tanx)dx

Evaluate: intsqrt(("cosec"x-cotx)/("cosec"x+cotx).(secx)/sqrt(1+2secx) dx

intsqrt(secx+1)dx