# Integral of $$$2 x$$$

Related calculator: Definite and Improper Integral Calculator

### Your Input

**Find $$$\int 2 x\, dx$$$.**

### Solution

**Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$** with $$$c=2$$$ and $$$f{\left(x \right)} = x$$$:

$${\color{red}{\int{2 x d x}}} = {\color{red}{\left(2 \int{x d x}\right)}}$$

**Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$** with $$$n=1$$$:

$$2 {\color{red}{\int{x d x}}}=2 {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}=2 {\color{red}{\left(\frac{x^{2}}{2}\right)}}$$

Therefore,

$$\int{2 x d x} = x^{2}$$

Add the constant of integration:

$$\int{2 x d x} = x^{2}+C$$

**Answer:** $$$\int{2 x d x}=x^{2}+C$$$