Integrate dy/dx = 2x/(x^2-4)
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 = x2-4 (the denominator).
When we differentiate this we get du/dx = 2x, therefore dx = 1/(2x) du.
If we substitute this back into the original equation: 2x/(x^2-4) dx = 2x/u 1/(2x) du.
The 2x cancels with the 1/(2x) leaving the integral of 1/u du.
Using our knowledge of integrals this equals ln u (the natural logarithm - log base e).
We now substitute x2 - 4 back in for u leaving y = ln(x2 - 4), the solution.
WR
Related Maths A Level answers
All answers ▸The Curve C shows parametric equations x = 4tant and y = 5((3)^1/2)(sin2t) , Point P is located at (4(3)^1/2, 15/2) Find dy/dx at P.
Determine the first derivative of the following curve defined by parametric equations x = 20-5t and y = t^5.
Show that arctan(x)+e^x+x^3=0 has a unique solution.
A curve has parametric equations: x = 3t +8, y = t^3 - 5t^2 + 7t. Find the co-ordinates of the stationary points.