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split the integral into (x^4)/(x^2) and (3x)/(x^2) which becomes x^2 and 3*(1/x). These can now be integrated separately and added together after the integration.

first integral: raise the power fo...

Re-arrange (1) : y = 2x + 4 Square both sides: y^2 = 4x^2 + 16 Substitute (1) into (2) and simplify: 2x^2 + 9x + 4 = 0 Factorise the equation: (2x+1)(x+4) = 0 Solve for x: x = -1/2 and x = -4 Substitute t...

To answer this we must remember that the derivative at a point on a curve, in this case x^2, is simply the value of the gradient of the line that just touches that point on the line. We can start by appro...

To solve this, we must use integration by parts as we can’t solve it directly. The formula for integration by parts is integral(UdV)=UV-integral(V*dU). The trick with this is to set dV=1 and to s...

Make use of identity sech^2(x) = tan^2(x) + 1

=> 2{tan^2(x) + 1} = 3 + tan(x)

Multiply out brackets and rearrange

=> 2tan^2(x) - tan(x) - 1 = 0

Use quadratic formula w...