$$f(x) = 3 + \int\limits_0^{2x} \tan t ~\mathrm{d} t$$
Like I already know how to find arctan in sigma notation, but how do I find the maclaurin series for tangent?
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Do you mean a formula for the general term or how to find its expansion at a given order? – Bernard May 12 '17 at 21:23
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how to find at a given order – gohn May 12 '17 at 21:24
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Perform the division by increasing powers of the expansion of $\sin x$ by the expansion of $\cos x$ up to this order. – Bernard May 12 '17 at 21:27
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1See https://math.stackexchange.com/a/286540/362009 – B. Goddard May 12 '17 at 21:45
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Note that $\int \tan(t) dt =\int \dfrac{\sin(t)dt}{\cos(t)} =\int \dfrac{(-\cos'(t))dt}{\cos(t)} $
Look familiar?
marty cohen
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