Partial Fractions Help: Integrating √(1+x^2)/x for Homework

Moenga
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Homework Statement


∫▒√(1+x^2 )/x dx


Homework Equations





The Attempt at a Solution


I don't know how to break this up. I know we break partial fraction problems up based on their denominator, however the denominator i this problem is just 'x'.
 
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Moenga said:

Homework Statement


∫▒√(1+x^2 )/x dx


Homework Equations





The Attempt at a Solution


I don't know how to break this up. I know we break partial fraction problems up based on their denominator, however the denominator i this problem is just 'x'.

Just write it as the sum of two fractions. No partial fractions needed.
 
I know its simple to do it that way. The problem is asking to use partial fractions
 
That problem is not appropriate to partial fractions. The method makes no sense for it.
 
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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