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Question Number 181643 by Frix last updated on 28/Nov/22

$$\mathrm{\Omega }=\underset{0}{\stackrel{\frac{\pi }{2}}{\int }}{\tan }^{-1}\cos xdx$$$$({\mathrm{I}}^{\prime }\mathrm{d}\mathrm{need}\mathrm{the}\mathrm{exact}\mathrm{value}\mathrm{if}\mathrm{possible}.{\mathrm{I}}^{\prime }\mathrm{ve}$$$$\mathrm{got}\mathrm{no}\mathrm{idea}\mathrm{if}\mathrm{and}\mathrm{how}\mathrm{this}\mathrm{can}\mathrm{be}\mathrm{solved}.)$$

Commented by MJS_new last updated on 28/Nov/22

$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{possible}\mathrm{to}\mathrm{solve}\mathrm{the}\mathrm{integral}\mathrm{but}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{very}$$$$\mathrm{complicated}\mathrm{and}\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{think}\mathrm{you}\mathrm{could}\mathrm{use}$$$$\mathrm{the}\mathrm{exact}\mathrm{value}.$$$$\mathrm{\Omega }\approx .845291$$$$\mathrm{www}.\mathrm{wolframalpha}.\mathrm{com}\mathrm{gives}\mathrm{the}\mathrm{exact}$$$$\mathrm{indefinite}\mathrm{integral}\mathrm{which}\mathrm{needs}\mathrm{about}25$$$$\mathrm{lines}\mathrm{but}\mathrm{only}\mathrm{an}\mathrm{approximate}\mathrm{value}\mathrm{for}[0;\pi /2]$$

Commented by Frix last updated on 28/Nov/22

$$\mathrm{Ok}\mathrm{I}\mathrm{see}...$$

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