Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.3 Derivatives Of Inverse Functions; Derivatives And Integrals Involving Exponential Functions - Exercises Set 6.3 - Page 433: 74

$=\int{x^{2}dx}=\frac{1}{3}x^{3}+C$

$2ln(x)$ can be written as $ln(x^{2})$ by bringing the constant multiplier into the logarithm. This leaves $e^{ln(x^{2})}$, which equals simply $x^{2}$. This leaves $$\int{x^{2}dx}=\boxed{\frac{1}{3}x^{3}+C}$$