Question
The integral x^2 (x ^2 x+ x ) (x x+1)^2 d x is equal to
BITSAT
Mathematics
Definite Integration
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. - x^2 x x+1 +c
- B. 2 _e|x x+ x|+c
- C. - x^2 x x+1 +2 _e|x x+ x|+c
- D. x^2 x^2 x-1 -2 _e|x x+ x|+c
Answer
C. - x^2 x x+1 +2 _e|x x+ x|+c
Step-by-step solution
(c) We note that d d x (x x+1)=x ^2 x+ x integrating by parts with x^2 as first function, we get aligned & I= x^2 x ^2 x+ x (x x+1)^2 d x \\ & =x^2 (- 1 x x+1 )- 2 x (- 1 x x+1 ) d x \\ & =- x^2 x x+1 +2 x x x x+ x d x \\ & =- x^2 x x+1 +2 _e|x x+ x|+c \\ & ( d d x (x x+ x)=x x ) aligned
Related: Mathematics — Definite Integration · All PYQ Banks