cos(a*x) + cos(x)
how do integrate this?
>>8098821
Cos(ax + x) and go from there
>>8098821
fuck i meant
cos(a*x)*cos(x)
>>8098821
Parts.
>>8098821
(a cos(x) sin(ax) - sin(x) cos(ax))/(a^2-1)
>>8098821
Convert to complex
Integrate by parts.
>>8098821
sin(ax)/a + sin x
+ C
>>8098821
Is he okay?
Divide and multiply the integrand by 2, and use product to sum transformation formulae.
2cosAcosB = cos(A+B) + cos(A-B)
Rest is easy.
>>8098821
Are you retarded?
[math] \displaystyle \int (\cos(ax)+\cos(x))dx=\int \cos(ax)dx+\int \cos(x)=\frac{\sin(ax)}{a}+\sin(x) [/math]
>>8098977
Are you OP?
>>8098977
Transformation formulae come in handy when integrating trigonometric functions.
>>8098979
>>8098982
Do you consider math to be a contest to see who can come up with the most convoluted solutions possible? It's like the IRL version of that image from the engineering maths textbook where they obfuscate 1+1=2 with series and the like.
You're suggesting integration by parts to integrate a cosine function.
>>8098982
you don't have to memorize this shit, op, just derive them using Euler's formulas
>>8098821
> yfw this problem is really easy with rational trig functions.
