--- title: Integration Rules --- ## Integration Rules As with differentiation, we use a variety of rules when integrating functions. Below are a few of the most common. **The Constant Rule:** ∫k dx = kx + C where k is a constant **The Power Rule:** ∫ xⁿ dx = + ^xⁿ⁺¹⁄_n+1 + C when n ≠ 1 **Exponential Rule:** ∫ e^kx dx = ¹⁄_kx e^kx + C where k is a constant **Trigometric Rules:** ∫ cos(x) dx = sin(x) + C ∫ sin(x) dx = -cos(x) + C **Sum/Difference Rules:** ∫[f(x) + g(x)]dx = ∫f(x)dx + ∫g(x)dx ∫[f(x) - g(x)]dx = ∫f(x)dx - ∫g(x)dx **Physical Calculus Rules:** ∫ v dt = x + C, where x is the displacement and v is the velocity ∫ a dt = v + C, where v is the velocity and a is the acceleration a = ^d⁄_dx(0.5v²) where a is the acceleration, and v is the velocity ∫ a dx = 0.5v² a + C = 0.5v² #### More Information: [Basic Rules with Examples](http://archive.learnhigher.ac.uk/resources/files/Numeracy/Integration_webversion.pdf) [In Depth Guide to Integrals](http://tutorial.math.lamar.edu/pdf/Calculus_Cheat_Sheet_Integrals.pdf)