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When you are asked to integrate a function f(x), you are really being asked the question: "what function F(x) exists such that when you take its derivative, you are left with f(x)?"

Let u...

We know that d / dx (x) = 1. Looking at x^2 as a specific example, and using the product rule, we see that d/dx(x^2) = xd/dx(x) + d/dx(x)x = x + x = 2x. Similarly for x^3, d/dx(x^3) = 3 * x^2 * d/dx(x) = ...

Rearrange first equation to show y=-5/3x-1

lines are parallel therefore gradient is the same

m=-5/3

First "Separate the Variables" by rearranging the equation to get the ys on the LHS and the xs on the RHS:

(1/y) dy=x dx

Now Integrate:

Integral(1/y) dy = Integral(x) dx

First it is necessary to notice that 4x^2-9 can be written as (2x-3)(2x+3). To solve this question, you first have to write all the fractions in terms of their lowest common denominator. In this case that...