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I'll show you on a whiteboard or a piece of paper, there's a nice grid method you can use which is a lot easier (I think) than the weird long division way I got taught in school.

The question tells us the ratio between two algebraic expressions is the same as the ratio between 2 other algebraic expressions. So, we can re-write the equation as (2x-1)/(x-4) = (16x+1)/(2x-1)Re-arrang...

Start by differentiating x² – 3xy – 4y² + 64 = 0 with respect to x to obtain an equation in x, y and dy/dx:
2x – 3y – 3x.dy/dx – 8y.dy/dx = 0 [use the product rule to differe...

As we are integrating, we must decide which method to use. As the integrand is of the form f(x)*g(x), integration by parts seems to make sense. Firstly, let L = INT(sin(x)*e^x). So we want to find L - thi...