Solving Indefinite Integral: Approach and Techniques

nissan4l0
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Homework Statement


Solve the indefinite integral


Homework Equations


\int\frac{dy}{y(1-y)}

How do I best approach this problem? I have been stuck for hours!
 
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Use partial fractions. That is write 1/(y(1-y)) as:

<br /> \frac{a}{y}+\frac{b}{1-y}

and determine the constants a and b.
 
Ok, thank you! I am taking a differential equations class but I have forgotten about the method of partial fractions. I will relearn it, and I will post my solution shortly.
 

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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