Is 5/((t)(1+4t+4t^2)) the correct solution for my calculus problem?

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1/ ((t) (1 + 4t + 4t ^2)) + 4 / (1 + 4t + 4t ^2)


= 5/ ((t) (1 + 4t + 4t ^2))
 
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No, it's not correct. To add these two rational expressions you need to find the least common denominator.
 
Why are you posting these problems in the Calculus and Higher forum? They should go in the Precalculus forum.
 
Because my problem has to do with calculus.
 

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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