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2x² + 7x + 6 step 1: find 2 numbers which times to make 12 and add to make 7, ans 3 and 4 step 2: rewrite equation as follows. 2x² +4x +3x +6step 3 factorize into: 2x(x+2) + 3 ( x+2)...

integrate using substitution: (I = the symbol for integration)let u = 2x + 5 therefore x = (u - 5)/2 du/dx = 2 which means that du = 2dx ---> dx = 1/2 duThis means that the integral now = I((u - 5)/2 x...

using the quotent ruledy/dx= (3(x^2+6)-3x(2x))/(x^2+6)^2dy/dx=3(x^2+6-2x^2)/(x^2+6)^2dy/dx=(18-3x^2)/(x^2+6)^2

You must expand the brackets and then handle each section separately x multiplied by x = x^2 x multiplied by 4 = 4x answer is x^2 + 4x

To find dy/dx, we must use a combination of the Product Rule and the Chain Rule.
If we let 3x^2=u and (x+2)^6=v, the Product Rule tells us that (uv)' = uv'+vu'
u'=6x, but to find v' we need to u...