# General Results for integration of reciprocal trig functions

As i'm currently revising for my maths A-level i decided to put together a table of general results for integration of trig functions. I came across $$\int cosec (kx)=-\frac 1k( \ln|cosec(kx)+cot(kx)|) dx +c$$ and $$\int cosec (kx)=\frac 1k( \ln|tan(\frac12kx) dx +c$$

I was wondering if these general results are valid for all k? and when i plotted both the graphs of the first result and second result of this integral, the graphs overlapped slightly in radians but fully when i plotted them in degrees? i vaguely remember being told calc. trig dosent work in degrees In the exam can i use either result when i have to integrate cosec kx or similar? and furthermore

$$\int sec (kx)=\frac 1k( \ln|sec(kx)+tan(kx)|) dx +c$$ and $$\int sec (kx)=\frac 1k( \ln|tan(\frac 12kx+\frac 14 \pi)|) dx+c$$

for any question could i just pick either result to use? are they both valid for all k and for all x? (yes i know both can be achieved by manual integration each time but i'm making a general results table to memorise to speed up answering questions as running out of time is my main problem in maths)

• Calculate the derivatives of the RHSs. – Martín-Blas Pérez Pinilla Apr 4 at 20:08
• Thanks, just checked them, the first 3 are correct, and the last one should read integral of sec(kx)=1/k(ln|tan(1/2kx)|)+c – Drew Doherty Apr 6 at 12:00
• The overlapping or not of of graphics is simply a consequence of the finite precision of floating-point numbers. – Martín-Blas Pérez Pinilla Apr 6 at 14:41