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Integrate dy/dx = 2x/(x²-4).

We can answer this question using integration by substitution, where we set u = something in terms of x.

In this case we are going to set u = x^2<...

b= 16-6a  this will be your substitution. 

5a- 2(16-6a)=19 now multiply out.

5a-32+12a=19 always remember positive and a negative multiplied is a negative.

17a=51

a= 51/17 = 3 ...

x² - 6x + 5 = 0.

For simple quadratic equations such as this example we need to factorise the expression into 2 brackets: (x+a)(x+b) = 0.

To find a and b we can expand the bracket...

Rewrite (8-9x)^(2/3) as (8(1-(9/8)x)^(2/3)=4(1-(9/8)x)^(2/3). Now apply the C4 binomial formula in the formula booklet, so: 4(1 - ((9/8)x)^(2/3)= 4[ 1 + (2/3)*((-9/8)x) + (2/3)((-9/8)x)^2 .....]= 4[ 1 - (...

p(x) = 2x⁵ + x⁴ – 26x³ – 13x² + 72x + 36
i) obtain the sum by using vieta's fomula: for p(x) the sum is hence -b/a hence, sum = -1/2
ii) obtain the ...