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Integral (t + 1 / t) ^ 3 / 2 (t ^ 2 - 1 / t ^ 2)dt?

Integral (t + 1 / t) ^ 3 / 2 (t ^ 2 - 1 / t ^ 2)dt.

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<img src="https://tex.z-dn.net/?

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Andreacr97

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<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0AI%3D-2u%2B%5Cfrac%7B1%7D%7B3%28u%5E2-1%29%5E3%7D%20%2B%5Cfrac%7B3u%7D%7Bu%5E2-1%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Cln%5Cleft%7C%5Cfrac%7Bu%2B1%7D%7Bu-1%7D%5Cright%7C%2BC%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7BI%3D-2%5Csqrt%7B%5Cfrac%7B1%2Bt%7D%7Bt%7D%7D%2B%5Cfrac%7Bt%5E3%7D%7B3%7D%2B3t%5Csqrt%7B%5Cfrac%7B1%2Bt%7D%7Bt%7D%7D%2B%5Cln%5Cleft%28%5Csqrt%7B1%2Bt%7D%2B%5Csqrt%7Bt%7D%29%2BC%7D%0A" />.