{"id":7907,"date":"2021-11-10T16:35:08","date_gmt":"2021-11-10T11:05:08","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7907"},"modified":"2021-11-10T22:21:52","modified_gmt":"2021-11-10T16:51:52","slug":"what-is-the-integration-of-1-x-log-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-integration-of-1-x-log-x\/","title":{"rendered":"What is the integration of 1\/x log x ?"},"content":{"rendered":"
We have, I = \\(\\int\\) \\(1\\over x log x\\) dx<\/p>\n
Put log x = t \\(\\implies\\) \\(1\\over x\\) dx = dt<\/p>\n
I = \\(\\int\\)\u00a0 \\(1\\over t\\) dt<\/p>\n
I = log | t | + C<\/p>\n
I = log |log x| + C<\/p>\n
Hence, the integration of \\(1\\over x log x\\) is log (log x) + C<\/p>\n
What is the integration of log cos x dx ?<\/a><\/p>\n What is the integration of log 1\/x ?<\/a><\/p>\n What is the integration of \\((log x)^2\\) dx ?<\/a><\/p>\n