Question

$\int x^2{e}^{x^3}.dx$ equals

• A. $\frac{1}{3}{e}^{x^2}+C$
  
• B. $\frac{1}{2}{e}^{x^3}+C$
• C. $\frac{1}{3}{e}^{x^3}+C$
  
• D. $\frac{1}{2}{e}^{x^2}+C$

Answer 1

The correct option is C $\frac{1}{3}{e}^{x^3}+C$


To find : $\int x^2{e}^{x^3}.dx$

Let $x^3=t$

Differentiating both sides $w.r.t.x$

$3x^2=\frac{dt}{dx}\Rightarrow x^{2}dx=\frac{dt}{3}$

On subsitituting

$\int x^2{e}^{x^3}.dx=\int \frac{e^t}{3}dt$

$=\int \frac{e^t}{3}+C$

$=\frac{e^{x^3}}{3}+C$

$\therefore option\left(A\right)$ is correct.