Ngô Quốc Anh

October 9, 2007

Một bài “khủng” về tích phân không xác định

Filed under: Các Bài Tập Nhỏ, Giải Tích 2 — Ngô Quốc Anh @ 23:36

Evaluate

\displaystyle\int \dfrac{1}{\sqrt { 1 - \sqrt {2 - \sqrt {3 - \sqrt { 4 - \sqrt x } } } }} dx.

Solution. Denote

\displaystyle u = \sqrt {1 - \sqrt {2 - \sqrt {3 - \sqrt {4 - \sqrt {x}}}}}

one can solve  x in terms of u and then try to evaluate

\displaystyle\int\frac {1}{u}dx.

Note that the integrand is just a polynomial.

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