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The key point in here is noticing that the derivative of sin(x) is cos(x). That way, if we rename sin(x) as u , i.e u:=sin(x), the derivative will be du=cos(x)dx. So, inside the integral, instead of havin...

Despite the hideous view, we can apply to this function the same methodology as all the other ones: break it down to pieces. What we mean is that we recognize three terms inside f(x): one is the number 1 ...

We know that a digit can be a number between 0 and 9. In this case, the first digit can't be 0, so it has to be a number between 1 and 9. So, we have 9 possible choices for the fi...