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∫ (ln(x)/(x*(1+ln(x))^2) dx

use u = 1+ln(x) as the substitution du/dx = 1/xdx = x du ∫ (ln(x)/(x*(1+ln(x))^2) dx = ∫ ((u-1) x/ x (u^2)) du = ∫ (u-1)/(u^2) du
JB
Answered by Jack B. • Maths tutor
8476 Views

Find the inverse function of f(x)=5/(x-4)

f(x) = 5/(x-4)To find the inverse, replace f(x) with y: y=5/(x-4)Now the aim is to make x the subject of the equation:Multiply both sides by x-4:y(x-4)=5Divide by y:x-4=5/yAnd finally add 4:x=5/y + 4
KM
Answered by Katy M. • Maths tutor
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Solve 5x - 2 > 3x + 11

Collect x terms together by moving them over the greater than sign to have 5x - 2 - 3x > 11 (moving terms is the same as with an equals sign, if it is positive on one side it will be negative on the other...
Answered by • Maths tutor
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ABC is a triangle with sides of length AB, 12m and BC,14m. Angle ACB = 43 degrees. Find the area of the triangle.

Use of the Sine Rule to ultimately work out the area of a triangleA/SinA = B/SinB14/Sin43 = 12/SinX14SinX = 12Sin43SinX = 12Sin43/14X=InverseSin(12Sin43/14) = 35.77-There are 180 degrees in triangle. Therefo...
EC
Answered by Eoin C. • Maths tutor
3967 Views

Using the substitution method, solve the following simultaneous equations 2y+3x=14 and 6x-y=8

Equation 1: 2y+3x=14 Equation 2: 6x-y=8 Rearrange Equation 2: y=6x-8 therefore 2y=12x-16 Substituting the rearranged equation 2 into equation 1: 12x-16+3x=14 15x-16=14 15x=30 x=2 Substituting x into equation...
AW
Answered by Alex W. • Maths tutor
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