Question

# The value of ∫x + 5(x − 2)2dx is :

A

ln|(x1)|7(x 2)+C

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

ln|(x2)|7(x 2)+C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

ln|(x2)|7(x 1)+C

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

ln|(x1)|7(x 1)+C

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C ln|(x−2)|−7(x − 2)+C We can see that the given expression is a proper fraction. Using partial fractions we'll split the given integrand as Ax − 2 + B(x − 2)2 One thing we should notice here is that in the expression one of the terms has (x - 2) whereas another has (x − 2)2. Can you guess why? Well, it's because if we had taken (x - 2) in the denominator for both A and B ,on taking the LCM we would have never got (x − 2)2 in the denominator. Thus we'll not get the same expression. We know that we always have to split our expression as sum of terms such that the expression won't change. Now let's take LCM and write the expression again- Ax − 2 + B(x − 2)2 = A(x − 2) + B(x − 2)2 On comparing the coefficients of like powers of x, with the given expression, we can say- A = 1 and B - 2A = 5 or B = 7 So, we'll have ∫1(x − 2) + 7(x − 2)2dx ln|(x−2)|−7(x − 2)+C

Suggest Corrections
0
Related Videos
Integration by Partial Fractions
MATHEMATICS
Watch in App