Question
$\int {{x^2}{e^{{x^3}}}dx}$ equals
- (a) $\cfrac{1}{3}{e^{{x^3}}} + C$
- (b) $\cfrac{1}{3}{e^{{x^2}}} + C$
- (c) $\cfrac{1}{2}{e^{{x^3}}} + C$
- (d) $\cfrac{1}{2}{e^{{x^2}}} + C$
Integrals — Class 12 Maths Solution
Step-by-step Solution
Option a is correct
Let $I = \int {{x^2}{e^{{x^3}}}} dx$
Put ${x^3} = t$ $\Rightarrow$ $3{x^2}dx = dt$
$\therefore$ $I = \cfrac{1}{3}\int {{e^t}dt} = \cfrac{1}{3}{e^t} + C = \cfrac{1}{3}{e^{{x^3}}} + C$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Integrals. Curated by Sachin Sharma. Free for all students.