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First of all note the dx means that we are integrating with respect to x.

So lets integrate each term seperately..

3x^2 ---> (raise the power by one then divide by the ne...

Fristly, we should integrate the whole equation,

y=∫ 6-8x+x^4 dx

y=6x-4x^2+x^5/5+C

Then, subsitituting values to find the C,

4=61-41^2+1...

As we have to differentiate both x and y, we must use implict differentiation for the y by differentiating it with respect to x (also written as d/dx)

5x² -> 10x (multiply t...

I think it’s best I work through an example with you as these problems can vary quite a lot, but the general methods used are the same.
Example: Use the substitution u=x²+5 to find: The in...

y = 5x² - 4/x³

1/x can be written as x^-1, which means our equation can also be written as y = 5x² - 4x^-3.

dy/dx means ...