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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

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

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 ot...

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. Ther...

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...