Trig Integral: integral of ( cos x + sin x ) / ( sin 2x ) dx

[grapz]

Can someone show me how to do this integral:

Integral of ( cos x + sin x ) / ( sin 2x ) dx

I tried using double angle identity for sin2x then i split up the fraction into two and i ended up with

1/2 integral ( sin x ) ^ -1 + ( cos x) ^ -1. But i do not know how to integrate ( sin x ) ^ -1

thanks

 

[soroban]

Re: Integral of a trig function

Hello, grapz!

Can someone show me how to do this integral? . \(\displaystyle \int \frac{\cos x + \sin x }{\sin2x}\,dx\)

I tried using double angle identity for \(\displaystyle \sin2x\) then i split up the fraction into two and i ended up with:

. . \(\displaystyle \frac{1}{2}\int\left(\frac{1}{\sin x} + \frac{1}{\cos x}\right)\,dx\) . . . . . Good!

\(\displaystyle \text{You have: }\;\frac{1}{2}\int\left(\csc x + \sec x)\,dx \qquad \hdots \quad Go\:f\!or\:it!\)

 

[grapz]

Re: Integral of a trig function

Ah right, i failed to realize that