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]

>>8098973
>>8098831

Ok

>>8098969
>>8098907
What?

>>8098977
Are you OP?

File: 13885339868_f3e26a67c5_o.jpg (75KB, 350x346px) Image search: [Google]

75KB, 350x346px

>>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.