Skip to content

The sine and cosine integrals are integrated to #1530

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
Rafael-SOWNet merged 1 commit into from
Sep 28, 2026
Merged

The sine and cosine integrals are integrated to #1530

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
17 changes: 17 additions & 0 deletions BREAKING-CHANGES.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1654,6 +1654,23 @@ was refused, so each was read as a product with an undeclared variable
| `"Chi(1)".Simplify()` | `Chi` | `Chi(1)`, and `0.8378669409802082…` evaluated |
| `"Si(x)".Differentiate("x")` | `Si` | `sin(x) / x` |

### The sine and cosine integrals are integrated to

`sin(x)/x` was left unintegrated. A polynomial in sines and cosines of a linear, beside a
polynomial, over powers of linears is now integrated to `Si` and `Ci`: each monomial of the sines
and cosines is a sum of sines and cosines of multiples of the argument, and under `u` = the linear
each term is `u^m sin(q u)` or `u^m cos(q u)`, which is `Si(q u)` or `Ci(q u)` for `m = -1` and by
parts toward them below. Several linears are split into partial fractions over them first, and an
argument `a + b x^r` beside a power of `x` is the same question under `u = x^r`
([#1501](https://github.com/asc-community/AngouriMath/issues/1501)).

| Input | Was (2.5.0) | Now |
|---|---|---|
| `"sin(x)/x".Integrate("x")` | `integral(sin(x) / x, x)` | `Si(x) + C` |
| `"sin(x)^2/x".Integrate("x")` | `integral(sin(x) ^ 2 / x, x)` | `1/2 * ln(x) + -1/2 * Ci(2 * x) + C` |
| `"sin(x)/(x*(1+x))".Integrate("x")` | `integral(sin(x) / (x * (1 + x)), x)` | `Si(x) + -cos(1) * Si(1 + x) + sin(1) * Ci(1 + x) + C` |
| `"sin(a+b/x)/x".Integrate("x")` | `integral(sin(a + b / x) / x, x)` | `-(cos(a) * Si(b * 1 / x) + sin(a) * Ci(b * 1 / x)) + C` |

### A definite integral is the limit at a bound where its antiderivative is undefined

`integral(x * e^(-x), x, 0, +oo)` was `NaN`, this library's way of saying a value does not
Expand Down
3 changes: 3 additions & 0 deletions Sources/.editorconfig
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -666,3 +666,6 @@ file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed

[Tests/UnitTests/Convenience/TrigonometricIntegralTest.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n

[Tests/UnitTests/Calculus/TrigonometricIntegralIntegrationTest.cs]
file_header_template=\nCopyright (c) 2019-2026 Angouri.\nAngouriMath is licensed under MIT.\nDetails: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.\nWebsite: https://am.angouri.org.\n
Loading
Loading