Integral of cos(x)/(sin(x) + cos(x)) - LearnMathsFree

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In this video, we look at a unique method of solving the integral of cos(x)/(sin(x) + cos(x)) over the interval [0, pi/4], without using any substitutions!

NOTE: Although I did say at the end of the video that there are all sorts of tricks and strategies you can use for integrals like these, this is definitely not true in general -- in fact, many of the integrals you find in research (including some integrals in my own research!) do not have nice, closed form solutions like this one.

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Is there a way to solve it using elementary functions? I was thinking Taylor Series

but sometimes you just have to think smart sometimes and this is really interesting to solve in a different manner/strategy

duckymomo

There are a lot of tough integrals in my channel.

integrationbee

Thanks a lot

Nice method and great explanation.

Keep solving such interesting problems.

integrationbee

The answer of this sum if the limiits were not there is x/2+1/2log|sinx+cosx|+c

mathsgaming

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