Indefinite Integral Homework: Get a Hint to Evaluate It

zorro
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Homework Statement



How do I evaluate this?

gif.latex?\int\frac{cos7x-cos8x}{1+2cos^2x}dx.gif


A hint will do.
 

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Abdul Quadeer said:

Homework Statement



How do I evaluate this?

gif.latex?\int\frac{cos7x-cos8x}{1+2cos^2x}dx.gif


A hint will do.

Convert the expression using trig identities and then try by-parts integration or substitution.
 
Did you get the answer or you are just suggesting?
 
Yeah, looking at the answer, It looks like a few trig identities (particularly the denominator), and then integration by parts (many times). Be warned, the answer is rather ugly (many lines ugly...)

by any chance did this come up in a Fourier decomposition (I am looking at the graph of it)? :P
 
n1person said:
Yeah, looking at the answer, It looks like a few trig identities (particularly the denominator), and then integration by parts (many times). Be warned, the answer is rather ugly (many lines ugly...)

by any chance did this come up in a Fourier decomposition (I am looking at the graph of it)? :P

Looking at the answer? Where is it?
No it is not from Fourier decomposition.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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