Integral of x

1. Power Rule: The general rule for integrating xn (where $-1$) is:

   ∫xn dx=xn+1n+1+CFor example, the integral of x3x^3x3 would be:

   ∫x3 dx=x44+C

2. Sum Rule: You can also integrate sums term by term:

   ∫(x2+x) dx=∫x2 dx+∫x dx=x33+x22+C

3. Example with Constants: If you have a constant multiplied by a function, like $5x$, you can pull the constant out of the integral:

   ∫5x dx=5∫x dx=5(x22)+C=5×22+C

4. Definite Integrals: If you’re working with limits, say from $a$ to $b$, you would calculate the definite integral like this:

   ∫abx dx=[x22] ab=b22−a22​

Let me know if you’d like to dive into a specific type of integral!