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Use the substitution u=1+e^x to find the Integral of e^(3x) / (1 + e^x)

e x =u-1 so e 3x =(u-1) 3 and du/dx = e x so rearranging gives dx=e -x du Substituting all that information in the integral we get Integral ( (u-1) 3 / (u(u-1)) du ) which simplifies to Integral (u -2 +1/u)....
IP
Answered by Ismet P. • Maths tutor
12346 Views

Explain price elasticity of demand and how firms can exploit this.

Price elasticity of demand (PED) is defined as % change in quantity demanded / % change in price. This is also the slope of the demand curve. If PED is less than 1, we say that the demand for the good is ine...
TD
3428 Views

How do I write a strong introduction?

The introduction is often seen as an annoying hurdle, but it is crucial in giving the marker a strong first impression. Writing an unclear intro that considers a few possible arguments or approaches but does...
JG
3993 Views

The gradient of the curve at point (x,y) is given by dy/dx = [7 sqrt(x^5)] -4. where x>0. Find the equation of the curve given that the curve passes through the point 1,3.

I like this question because it can be broken down into parts, each which contain an important reminder/lesson for an A level/GCE maths student. I would start the lesson by running through the rules of indic...
MS
Answered by Michael S. • Maths tutor
4997 Views

Evaluate the 'First-Past-the-Post' Electoral voting system

FPTP is an electoral system used most notably in the UK General Election and the Indian Parliamentary Elections. Under this system the party with the most votes in each constituency/region wins that seat (i....
AC
Answered by Angus C. • Politics tutor
7851 Views