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y=(4x+1)^3*sin(2x) - this is a product of two functions of x. It can be rewritten as y = u(x)*v(x)   ; where u(x) = (4x+1)^3 and v(x) = sin(2x)

Using the product rule: dy/dx = u'(x)*v(x) + v'(x)*u(...

This question must be attempted by integration by parts since it cannot be integrated outright and we can thus change the integral to 1 times lnx. We can then use the formula for integration by parts of I...

First, recall that when integrating, squared trigonometric functions often cause issues. Therefore, use the identity: cos^2(x) = (cos(2x) + 1)/2 to remove this power, giving the integral: ∫ (xcos(2x))/2  ...

(Question from AQA A level maths specimen papers) When looking at this question, you need to appreciate the steps required in order to reach the final answer before diving straight in. Firstly, the questi...

Step 1: multiply (5sqrt(3)-6)/(2sqrt(3)+3) by (2sqrt(3)-3)/(2sqrt(3)-3) (this is a trick called CONJUGATION as you're really just multiplying the fraction by 1. Step 2: Expand and ...