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According to the rules of logarithms, when you take a log of something to the power of something, you multiply the log of the base by the power, so in this case, taking logs of both sides would give us...
First note that ln(x) = 1ln(x), this is in the form udv/dx.
Let dv/dx = 1 and u = ln(x).
du/dx = 1/x from the standard results and v = x by integration.
1. ʃ sinx*ln(cosx) dx
First notice the composition ln(cosx). To make the expression easier to integrate we try substitution (substitution is often useful when trying to integrate expressi...
Integration is the inverse of differentiation. I.e. for differentiation of linear expressions we multiply the coeifficient with the power of the unknown and then subract 1 from the power. Integration i...
As in every case dy/dx can be found by differentiating each term individually with respect to x.
Let's first tackle the 4x term.
As always the ...
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