What are some common integral formulas?

What are some common integral formulas I should know?

Some common integral formulas include:

1. ∫x^n dx = (x^(n+1))/(n+1) + C, for n ≠ -1
2. ∫e^x dx = e^x + C
3. ∫sin(x) dx = -cos(x) + C
4. ∫cos(x) dx = sin(x) + C
5. ∫1/x dx = ln|x| + C Would you like to know more about any specific formula?

Can you explain the integral of e^x?

Sure! The integral of e^x is quite straightforward. It is:

∫e^x dx = e^x + C

where C is the constant of integration. This is because the derivative of e^x is also e^x, making it unique among functions.

What about the integral of sin(x)?

The integral of sin(x) is:

∫sin(x) dx = -cos(x) + C

This means that when you integrate sin(x), you get -cos(x) plus the constant of integration C.

Are there any special techniques for solving integrals?

Yes, there are several techniques for solving integrals, including:

1. Substitution
2. Integration by parts
3. Partial fraction decomposition
4. Trigonometric identities
5. Numerical integration methods Would you like to dive deeper into any of these techniques?