How Do You Calculate the Maclaurin Series for log(1 + x^4)?

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Hi guys! I need your help , soon I have an exam.

I should do Maclaurin series of the log (1 + x^4) , but the only example that I have avoid some steps and I can't resolve.
Thank you!
 
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Can you find the serie of log(1+x)??
 
Im not very good in this...I feel ashame...can I use for instance log(1+x) and then I sustitue (1 + x^4) on it?
 
Do you know the definition of the MacLaurin series??
 

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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