Question
e^ x (1+x) ^ 2 (e^ x x ) dx equals
BITSAT
Mathematics
Indefinite Integration
2021
BITSAT 2021
BITSAT Mathematics Question (2021) — Solution
Options
- A. - (e x^ x )+ C
- B. (x e^ x )+ C
- C. (e^ x )+ C
- D. (e^ x )+ C
Answer
B. (x e^ x )+ C
Step-by-step solution
e^ x (1+x) ^ 2 (e^ x x ) dx Let x e^ x =t (x e^ x +e^ x )= dt dx d x= dt e^ x (x+1) e^ x (1+x) ^ 2 (e^ x x ) dx = e^ x (1+x) ^ 2 t d t e^ x (1+x) = 1 ^ 2 t dt = ^ 2 t dt = t+ C = (x e^ x )+ C
Related: Mathematics — Indefinite Integration · All PYQ Banks