Using partial fractions find the integral of (15-17x)/((2+x) (1-3x)^2 )

First seperate the function into the form A/(2+x)  +   B/(1-3x)   +   C/(1-3x)2 . Find A B and C by equating the intergral to {A(1-3x)+B(1-3x)(2+x) +C(2+x)}/(2+x)(1-3x) . Cancelling the denominators gives an equation equal to 15-7x, and in terms of A, B and C. We then use comparison of the right and left hand sides to find A, B and C. By subsituting x=-2, x=1/3 and by comparing coefficients of x2 the values of A B and C can be found. Subbing these into the partial fraction equation(1st line) we can then intergrate this expression, using the fact that the intergral of 1/x is equal to ln(x). 

SB
Answered by Sean B. Maths tutor

4860 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

4. The curve C has equation 4x^2 – y3 – 4xy + 2y = 0. P has coordinates (–2, 4) lies on C. (a) Find the exact value of d d y x at the point P. (6) The normal to C at P meets the y-axis at the point A. (b) Find the y coordinate of A


Can you show me why the integral of 1/x is the natural log of x?


How can you factorise expressions with power 3 or higher?


Find dy/dx for y=5x^3−2x^2+7x−15


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning