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I am trying to find the indefinite integral of sqrt(tanx) dx and the indefinite integral of sqrt(cos2x) dx. Any ideas? <p><b>Idea 1:</b> There seem to be no known closed form antiderivatives for the given functions (in terms of the elementary functions). However, the antiderivatives certainly exist; Expand the given integrand in terms of its Taylor series at x=0. Integrating the Taylor series term by term gives the Taylor series expansion of the antiderivative. <p><b>Idea 2:</b> Usually, one is interested in computing the definite integral. For this purpose, there are many numerical methods known. For example, Simpson's Rule.
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Prof. Ashay Dharwadker