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We can't integrate cos^2(x) as it is, so we want to change it into another form. We can easily do this using trig identities.

1) Recall the double angle formula:

c...

There's a nice trick here you can do, treat the equation as 1*ln(x) then intergrate by parts.

Differentiating ln(x) gives 1/x, while intergrating 1 gives x

So your left with...

First off, an explicit definition needs to be understood. An explicit definition is the standard form in which many equations are found:

y = f(x)        (1)

for example:  y=...

Often, it can seem daunting when you are asked to differentiate a function that looks particularly messy. However, it's really quite simple if you break it down in easy to manage steps....

How to integrate ln(x)?

In order to integrate log x of base e, we are going to apply integration by parts.

Recall that the formula for integration by parts i...