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Before we blindly start using the integration by parts formula, we can see that no matter how many times we differentiate or integrate sin(x) we will still have a trigonometric function. The aim of the 'b...

When integrating, we raise the power by 1 and divide by the new powerSo, 2x⁵ becomes 2x⁶ /6 which simplified down as the question asks is x^6/3-1/(4x³) is -(1/4)x^^-3<...

Composition of functions is when one function is inside of another function. That is, we replace each occurrence of x found in the outside function with the inside function. In our example, we start by wr...

y = x^3+3x-2dy/dx = 3x^2-2Stationary points when dy/dx = 00 = 3x^2-22 = 3x^2+-root2 = 3x+-root2/3 = x

4^(n)-1 factors to (2^(n)-1)(2^(n)+1) by difference of two squares by definition of a prime (only has factors 1 and itself (given that itself isn't 1))So Exactly one of the brackets should = 1 for 4^(n)-1...