evaluate the following indefinite integral.\n int 20x dx \n int 20x dx=square

Explanation:

Step1: Use integral constant - multiple rule

The integral of a constant times a function is the constant times the integral of the function, i.e., $\int kf(x)dx=k\int f(x)dx$. Here $k = 20$ and $f(x)=x$, so $\int 20x dx=20\int xdx$.

Step2: Apply power - rule for integration

The power - rule for integration is $\int x^n dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$). For $n = 1$ in $\int xdx$, we have $\int xdx=\frac{x^{1+1}}{1 + 1}=\frac{x^{2}}{2}$. Then $20\int xdx=20\times\frac{x^{2}}{2}$.

Step3: Simplify the result

$20\times\frac{x^{2}}{2}=10x^{2}+C$.

Answer:

$10x^{2}+C$