Table of Basic Integrals
2026ReferenceSergey
Reference table of the basic indefinite integrals of the elementary functions: power, exponential, logarithmic and trigonometric.
1
270
Search results for “integrals”
22 results
Integrals with Exponentials
2026ReferenceSergey
Reference table of indefinite integrals of the exponential function and its products with powers of x.
0
290
Integrals of Hyperbolic Functions
2026ReferenceSergey
Reference table of indefinite integrals of the hyperbolic sine, cosine, tangent and cotangent.
0
260
Integrals with Logarithms
2026ReferenceSergey
Reference table of indefinite integrals of expressions containing the natural logarithm.
0
230
Integrals of Rational Functions
2026ReferenceSergey
Reference table of indefinite integrals of rational functions, including quadratic denominators and partial-fraction forms.
0
290
Integrals with Radicals
2026ReferenceSergey
Reference table of indefinite integrals of expressions containing square roots and other radicals.
0
260
Integrals of Trigonometric Functions and Exponentials
2026ReferenceSergey
Reference table of indefinite integrals of products of exponentials with sine and cosine.
0
290
Integrals of Trigonometric Functions and Monomials
2026ReferenceSergey
Reference table of indefinite integrals of products of powers of x with sine and cosine.
0
290
Integrals with Trigonometric Functions
2026ReferenceSergey
Reference table of indefinite integrals of sine, cosine, tangent and their powers and products.
0
280
Vector calculus. Surface integrals of the second kind. Flux
2026Problem sheetSergey
The flux of a vector field through an oriented surface: the normal and the choice of side, the explicit and parametric forms, the lateral surface of a cylinder.
0
380
Vector calculus. Line integrals of the first kind
2026Problem sheetSergey
Integration with respect to arc length: parametrising a curve, the length element , arc length, curves in polar coordinates, the mass and centre of mass of a wire, symmetry instead of computation.
0
530
Vector calculus. Line integrals of the second kind. Work of a field
2026Problem sheetSergey
Integrating a vector field along a directed curve: parametrising a segment and a graph, the work of a force, path dependence, a potential field and its potential, a curl-free field in a domain that is not simply connected.
0
400
Vector calculus. Surface integrals of the first kind
2026Problem sheetSergey
Integration with respect to surface area: the area element for an explicit and a parametric surface, pieces of planes, the sphere in spherical coordinates.
0
340
The torsion component of the Picard scheme
2026OtherBogdan Zavyalov
Every finite flat commutative group scheme over a noetherian local ring is the torsion component of the Picard scheme of a smooth projective scheme with 3-dimensional fibers, built as a quotient of a complete intersection. An application: Hodge numbers that jump in a smooth projective family.
1
500
A curiosity: “supersmooth” varieties
2026TheorySean Cotner
A rigidity condition on schemes, strictly stronger than smoothness, introduced with examples and a look at where it fails to be geometric — no known application, just a curiosity.
1
120
An example of a non-reduced Picard scheme
2026TheorySean Cotner
An example, due to Serre, of a smooth projective surface in positive characteristic whose Picard scheme fails to be reduced, worked out via the two governing dimension inequalities.
1
170
@sean_cotner
NSF Research Fellow and postdoc at the University of Bonn. Previously an NSF Research Fellow and Postdoctoral Assistant Professor at the University of Michigan, and before that a graduate student at Stanford, advised by Brian Conrad. Interested in arithmetic geometry, algebraic groups (broadly construed), and integral questions connected to the local Langlands program.