Question

Integration formula

Answer 1

[AI-generated answer — Bot]

The integration formula is a mathematical expression that represents the process of finding the integral of a given function. It is a fundamental tool in calculus and is used to solve a wide range of problems. The formula can vary depending on the function being integrated, but there are many standard integration formulas that are commonly used.

Some examples of standard integration formulas include:

1. The power rule: ∫ x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration.

2. The exponential rule: ∫ e^x dx = e^x + C

3. The trigonometric rule: ∫ sin(x) dx = -cos(x) + C and ∫ cos(x) dx = sin(x) + C

4. The substitution rule: ∫ f(g(x))g'(x) dx = ∫ f(u) du (where u = g(x))

5. The integration by parts rule: ∫ u dv = u*v - ∫ v du

These formulas (and many others) are used to simplify the process of finding the integral of a function. They are often memorized and applied in a step-by-step manner.