Question

whats the.... (ill post it)

Answer 1

\[\int\limits_{}^{} \ln (x)\]

Answer 2

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Answer 3

integrate by parts. do this only once and then memorize it

Answer 4

it is one of those integrals that math teachers love to put on a test, or some variation of it, so it is really just best to memorize that the anti - derivative of the log is \(x\ln(x)-x\) we can word through the steps if you like

Answer 5

\[\int udv=uv-\int vdu\] put \(u=\ln(x), dv =1, v = x, du =\frac{1}{x}dx\) get
\[int \ln(x)=x\ln(x)-\int 1dx=x\ln(x)-x\]

Answer 6

remember in calc 1 when you kept seeing \(\frac{d}{dx}\sqrt{x}\) and at some point you stopped you stopped using the power rule and went right to \(\frac{1}{2\sqrt{x}}\) because you just knew it? same thing for this one