Integral of 1/(x^3 + 2x^2 -x - 2)
Factorise denominator using the factor theorem giving - 1/(x+1)(x+2)(x-1) Use partial fractions to turn this into an easier form to integrate giving - 1/3(x+2) + 1/6(x-1) - 1/2(x+1) using integral 1/x = ln(x) integrate each term seperately - 1/3 ln(x+2) + 1/6 ln(x-1) - 1/2 ln(x+1) + C Combine log terms using laws of logarithms - Answer: ln[ A(x-1)1/6 (x+2)1/3 (x+1)-1/2 ]
MO
Related Maths A Level answers
All answers ▸Integrate 5sinxcosx + 5cosx
How would you differentiate 3x^4 - 2x^2 + 9x - 1
The curve C has equation x^2 – 3xy – 4y^2 + 64 = 0; find dy/dx in terms of x and y, and thus find the coordinates of the points on C where dy/dx = 0
A curve has parametric equations x=t(t-1), y=4t/(1-t). The point S on the curve has parameter t=-1. Show that the tangent to the curve at S has equation x+3y+4=0.