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Before we start any integration steps it would be wise to try and simplify the fraction that we have been given. We want to get rid of that denominator so we will start by expanding out the numerator. Thi...

The composite function can be thought of as if the function f(x) is the variable for the function g(x) instead of x. So first you find the value of the function f(4),f(4) = 10 - (3x4) = 10 - 12 ...

1. The first step is to work out how many (1/6) there are in one whole. 6 x (1/6) = 1.
   2)The next step uses partitioning. Split the 4 & (1/2) into a separate (4) and then (1/2)
   3) Wo...

I would use the fact that ln is the inverse function of the exponential function e^x to re-write the equation as x=e^y. This can be directly seen by just putting e^y=e^(lnx). Since the definition of a ln(...

First, use the identity cos(2x)=(cos(x))^2-(sin(x))^2 along with the identity (sin(x))^2+(cos(x))^2=1 to obtain the integral of 1/2*(1-cos(2x)) as it is not possible to integrate (sin(x))^2 straight off w...