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I am looking at a solution to an integral using differentiation under the integral sign. So let ##\displaystyle f(t) = \frac{\log (tx+1)}{x^2+1}##. Then, through calculation, ##\displaystyle f'(t) = \frac{\pi t + 2 \log (2) - 4 \log (t+1)}{4(1+t^2)}##. The solution immediately goes to say that ##\displaystyle f(t) = \frac{\log (2) \arctan (t)}{2} + \frac{\pi \log (t^2+1)}{8} - \int_0^t \frac{\log (t+1)}{t^2+1} ~ dt##. Could someone make this step a bit clearer? How does the LHS just become ##f(t)##?