Question
The value of 1 [(x-1)^3(x+2)^5 ]^ 1 4 d x, is
BITSAT
Mathematics
Indefinite Integration
2022
BITSAT 2022
BITSAT Mathematics Question (2022) — Solution
Options
- A. 4 3 ( x+1 x-2 )^ 1 4 +C
- B. 3 4 ( x-1 x+2 )^ 1 4 +C
- C. 4 3 ( x-1 x+2 )^ 1 4 +C
- D. 1 3 ( 2 x-1 4 x-3 )^ 1 4 +C
Answer
C. 4 3 ( x-1 x+2 )^ 1 4 +C
Step-by-step solution
I= 1 ( x-1 x+2 )^ 3 / 4 (x+2)^2 d x Let x-1 x+2 =t 3 d x (x+2)^2 =d t aligned I & = 1 3 1 t^ 3 / 4 d t= 1 3 ( t^ 1 / 4 1 / 4 )+C \\ & = 4 3 t^ 1 / 4 +C= 4 3 ( x-1 x+2 )^ 1 / 4 +C aligned
Related: Mathematics — Indefinite Integration · All PYQ Banks