Question

timed problem
score: 3/10
$int 2x^{2} dx$
answer
$\frac{2}{3}x^{3}+c$
$4x+c$
$x^{3}+c$
$4x^{3}+c$

Explanation:

Step1: Factor out the constant

$\int 2x^2 dx = 2\int x^2 dx$

Step2: Apply power rule for integration

The power rule is $\int x^n dx = \frac{x^{n+1}}{n+1} + C$ for $n
eq-1$. Here $n=2$, so:
$2\times\frac{x^{2+1}}{2+1} + C = 2\times\frac{x^3}{3} + C$

Step3: Simplify the expression

$\frac{2}{3}x^3 + C$

Answer:

$\frac{2}{3}x^3 + C$ (Option 1: $\frac{2}{3}x^3 + C$)