মান নির্ণয় করঃ∫³₂dx/((x-1)√(x²-2x))

$\int_{2}^{3} \frac{d x}{(x-1) \sqrt{x^{2}-2 x}} ; \int_{2}^{3} \frac{d x}{(x-1) \sqrt{(x-1)^{2}-1}}$

মনে করি, $\mathrm{x}-1=\mathrm{z} \quad \therefore \mathrm{dx}=\mathrm{dz} ; \quad \mathrm{x}=2$ হলে, $\mathrm{z}=1 ; \mathrm{z}=3$ হলে, $\mathrm{z}=2$

$\int_{1}^{2} \frac{\mathrm{dz}}{\mathrm{z} \sqrt{\mathrm{z}^{2}-1}}=\left[\sec ^{-1} \mathrm{z}\right]_{1}^{2}=\left[\sec ^{-1} 2-\sec ^{-1} 1\right]=\frac{\pi}{3}-0=\frac{\pi}{3}$