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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
12314 Views

There are 25 CD's in a box and an individual orders 14 boxes. How many CD's did the person order in total

as there are 25 CD's in one box, then we would multiply by 14 to know the total number of CD's, we use multiplication as it is quicker than adding 25 14 times. I would then show the column multiplication met...
AB
Answered by Aisha B. • Maths tutor
3101 Views

Factorise x^2 + 4x + 4

Factorising takes the form of (x+a)(x+b) where in this case: a+b = 4 anda*b=4this is taken from the original equations coefficient to x and the constant value.factorising gives (x+2)(x+2) which is equivalent...
RS
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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
4966 Views

show that the value of cos(30) x tan(60) + sin(30) is an integer

cos(30) x tan (60) + sin (30) = (√3)/2 x √3 + 1/2 = 3/2 + 1/2 = 4/2 = 2
HP
Answered by Henry P. • Maths tutor
14386 Views