1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The value of ∫(x−1)(x−2)(x−3)(x−4)(x−5)(x−6) dx is (where ′C′ is the constant of integration)

A
x+3ln|x4|24ln|x5|+30ln|x6|+C
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
x+3ln|x4|12ln|x5|+30ln|x6|+C
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x+3ln|x4|12ln|x5|+36ln|x6|+C
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
x+12ln|x4|24ln|x5|+30ln|x6|+C
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A x+3ln|x−4|−24ln|x−5|+30ln|x−6|+C I=∫(x−1)(x−2)(x−3)(x−4)(x−5)(x−6)dx =∫[1+(x−1)(x−2)(x−3)(x−4)(x−5)(x−6)−1]dx =∫[1+(x−1)(x−2)(x−3)−(x−4)(x−5)(x−6)(x−4)(x−5)(x−6)]dx =∫[1+3×2×1(x−4)(−1)(−2)+4×3×2(1)(x−5)(−1)+5×4×3(2)(1)(x−6)]dx =∫[1+3(x−4)−24(x−5)+30(x−6)]dx =x+3ln|x−4|−24ln|x−5|+30ln|x−6|+C

Suggest Corrections
3
Join BYJU'S Learning Program
Related Videos
Integration by Partial Fractions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program