Have i integrated this correctly?

Dell · 2009-01-26T15:48:49+00:00

\int(x-5)/(x2-2x+2)dx (x-5)/(x2-2x+2)=(x-1-4)/((x-1)2+1) x-1=t therefore x=t+1 dx=x'dt=(t+1)'dt=dt \int(x-5)/(x2-2x+2)dx=\int(t-4)/(t2+1)dt =\intt/(t2+1)dt-4\int1/(t2+1)dt =0.5ln|t2+1|-4arctg(t)+c

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

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