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Answer: (x^3)/3 + x^2 +5 ln (x) .

The general equation of a circle takes the form (x - A)^2 + (y - B)^2 = r^2 where (A,B) is the centre of the circle with radius r. Thus, we aim to rearrange the equation in the question to match this form. S...

Use the cosine trig identity, cos(a-b)=cos(a)cos(b)+sin(a)sin(b) ,to write Rcos(x-a) as R(cos(x)cos(a)+sin(x)sin(a)).Now we can equate the coefficients of the sines and cosins on either side of the equation ...

When we work with circles, one of the most popular things to pop up is pi. We know that for any circle the circumference divided by the radius gives pi, without failure always. Pi is a number that’s been fou...

One of the best ways to view dy/dx is as a fraction. When we have y=f(g(x)), we need to make a substitution u=g(x) to find dy/dx. This leaves us y=f(u) and u=g(x). Differentiating said terms leaves us with d...