How do you integrate sec(5/2x) tan(5/2x) dxsec(52x)tan(52x)dx?

1 Answer
Apr 21, 2015

Personnaly i don't use the sec(x)sec(x) function

u = 5/2xu=52x
du = 5/2du=52

int1/cos(5/2x)*sin(5/2x)/cos(5/2x)dx = 2/5int1/cos(u)*sin(u)/cos(u)du1cos(52x)sin(52x)cos(52x)dx=251cos(u)sin(u)cos(u)du

2/5intsin(u)/cos^2(u)du =-2/5int- sin(u)*cos^-2(u)du25sin(u)cos2(u)du=25sin(u)cos2(u)du

We have : u'*u^n

Remember the formula intu'u^n = 1/(n+1)*u^(n+1)

-2/5int1/(-2+1)*cos^(-2+1)(u) = -2/5int-1/cos(u)du

=>2/5[1/cos(5/2x)]+C