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We use integration by parts. Set $u = x$ and $dv/dx = e^x$. This leads to $du/dx = 1$, and $v = e^x$. Then:\begin{align*}\int xe^x \mathop{\mathrm{d}x} &= xe^x - \int e^x \mathop{\mathrm{d}x}\&= x...

This is one of the most common a level math question. One which is essential to understand as it gives a firm understanding of core fundamental principles in math which are Completing the square and Algeb...

Explain to the students what a one to many functions is which in this case is a quadratic, giving them an understanding of why there are two solutions, aided with the image of the quadratic.
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To solve this equation we will need to apply the chain rule. This states that:dy/dx = dy/du * du/dxTo make the question simpler, we shall let u = x⁴+ x, and so:y = u¹⁰ and u = x^...

Firstly, we can divide through by 2 to get a simpler form of the equation: x^2-7x+6=0. To solve this quadratic equation we need to factorise it. We do this by splitting it up into two brackets which would...