(a) Express 9x+11/(2x+3)(x-1) as partial fractions and (b) find the integral of 9x+11/(2x+3)(x-1) with respect to x
(a) 9x+11/(2x+3)(x-1) = A/2x+3 + B/x-1
9x+11 = (x-1)A + (2x+3)B
Setting x=1 gives B=4, setting x=-3/2 gives A=1
so the final answer is 1/(2x+3) + 4/(x-1)
(b) 1/2ln|2x+3| + 4ln|x-1| + c
AT
Related Maths A Level answers
All answers ▸The curve C has equation 4x^2 – y^3 – 4xy + 2^y = 0 The point P with coordinates (–2, 4) lies on C . Find the exact value of dy/dx at the point P .
The points A and B have coordinates (1, 6) and (7,− 2) respectively. (a) Find the length of AB.
Express (5sqrt(3)-6)/(2sqrt(3)+3) in the form m+nsqrt(3) where m and n are integers. [Core 1]
What is a logarithm?