How does the integration of lnsinx work

[raw gulch]

I need help with this one, thanks

[cyan plaza]

If you want to integrate between 0 and pi/2, you can u sub to get the integral of ln cos instead, then add both to get ln((sin 2x) /2) . Finally, split the ln and notice that ln(sin) is symmetrical along x=pi/2

[wooden bronze]

substitute x as sin-1 t

[raw gulch]

Without the limits is a lot harder right?

[steady dust]

i think impossible mabye

[digital sorrel]

likely non elementary ig

with limits, we can work out with kings rule or smth

[covert vessel]

ln sinx has no antiderivative that uses elementary functions

your best bet is to just do a reimann sum with very small intervals

or have a calculator do it for you

[raw gulch]

Right, thanks