| Copyright | Copyright 2025 Yoo Chung |
|---|---|
| License | Apache-2.0 |
| Maintainer | dev@chungyc.org |
| Safe Haskell | None |
| Language | GHC2021 |
Symtegration.Integration.Parts
Description
Synopsis
- integrate :: [Text -> Expression -> Maybe Expression] -> Text -> Expression -> Maybe Expression
Documentation
Arguments
| :: [Text -> Expression -> Maybe Expression] | Integration algorithms to try on the parts. |
| -> Text | Symbol for the variable. |
| -> Expression | Expression to integrate. |
| -> Maybe Expression | Integral, if derived. |
Integrates by parts.
Specifically, if for
\[ \int f g \, dx \]
it is the case that we can find \(F = \int f \, dx\) and \(\int F \frac{dg}{dx} \, dx\), then we can derive the integral as
\[ \int f g \, dx = F g - \int F \frac{dg}{dx} \, dx \]
>>>let directMethods = [Powers.integrate, Trigonometric.integrate]>>>toHaskell . simplify <$> integrate directMethods "x" ("x" * cos "x")Just "x * sin x + cos x"