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Completing the square refers to the process of rewriting a general quadratic expression into the form of a(x+b)² + c.For example we are asked ...

We can use substitution for this one. Take y=ln(x) to be equal to y= 1 x ln(x)Set u=ln(x) and dv/dx=1Compute du/dx and v:du/dx=1/x and v=xUse given formula - ∫ udv/dx dx = uv - ∫ vdu/dx dx= xln(x) - ∫ x/x...

a²=b²+c²

We can differentiate the terms separately:
The first term e^10x can be differentiated using the chain rule.
Let u = 10xWe can differe...

The first step is to notice that this is a standard integral in the form of 1/(x^2+a^2). In order to reach this form, we must first complete the square. Then we have 1/(x+2)^2-4+13=1/(x+2)^2+9. We can the...