wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Integrate the rational function x(x2+1)(x1)

Open in App
Solution

Let x(x2+1)(x1)=Ax+B(x2+1)+C(x1)

x=(Ax+B)(x1)+C(x2+1)

x=Ax2Ax+BxB+Cx2+C

Equating the coefficients of x2,x, and constant term, we obtain
A+C=0

A+B=1

B+C=0

On solving these equations, we obtain

A=12,B=12, and C=12

From equation (1), we obtain

x(x2+1)(x1)=(12x+12)x2+1+12(x1)

x(x2+1)(x1)=12xx2+1dx+121x2+1dx+121x1dx

=142xx2+1dx+12tan1x+12log|x1|+C

Consider 2xx2+1dx, let (x2+1)=t2xdx=dt

2xx2+1dx=dtt=log|t|=log|x2+1|

x(x2+1)(x1)=14log|x2+1|+12tan1x+12log|x1|+C

=12log|x1|14log|x2+1|+12tan1x+C

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Real Valued Functions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon