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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 expressions that are or incl...

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 is the ...

Start by making a note of each topic that may come up in your exam. You can find these in your textbook or revision guide. Let me know if you need help finding the list of topics that your exam board uses. T...

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 derivative can be found by multiplying the term by the power of ...

Using the completing the square method: 1. Notice (x+4) 2 = x 2 + 8x +16 which differs from the question by a constant 2. So we can write: x 2 + 8x + 3 = (x+4) 2 - 13 (check this yourself if you don't see it...