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dx=du/6 => (u-5)/6=x So the integral is now (2((u-5)/6)-3)(u^1/2) du/6 Which through simplifying becomes (1/36)(2u-28)(u^1/2)du = (1/36)(2u^3/2 -28u^1/2)du After integrating becomes (1/36)(4(u^5/2)/5 -...

The best method to revise is through solving past questions and timed exam papers. As long as you have your notes and understand all the basic principles, then you just need to practice in order to avoid ...

Let $ denote the integral symbol, as I am limited here by my keyboard.

Recall the formula for integration by parts:

$ u.(dv/dx) dx = uv - $ u(dv/dx) dx

So to find $^pi_0...

We shall differentiate each term in the equation with respect to x.

dy/dx (x²) = 2x

dy/dx (2y²) = 4y dy/dx

dy/dx (3x) = 3

So we now have the equation 2x +...

Multiply everything through by e^x   and rearrange so it equals zero
you now have e^2x -e^x-6=0
It is now similar to a quadratic equation, make the dummy substitu...