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 ▸How do you calculate the angle between two vectors?
How do you find the gradient of a curve?
What is a derivative and how do we calculate it from first principles?
A curve has equation y = 2x^5 + 5x^4 1 . (a) Find: (i) dy/ dx [2 marks] (ii) d^2y/ dx^2 (b) The point on the curve where x ¼ 1 is P. (i) Determine whether y is increasing or decreasing at P, giving a reason for your answer.