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2. Integration by parts - Wikipedia

   en.wikipedia.org/wiki/Integration_by_parts

   Integration by parts is a heuristic rather than a purely mechanical process for solving integrals; given a single function to integrate, the typical strategy is to carefully separate this single function into a product of two functions u(x)v(x) such that the residual integral from the integration by parts formula is easier to evaluate than the ...

3. Integration by substitution - Wikipedia

   en.wikipedia.org/wiki/Integration_by_substitution

   In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation , and can loosely be thought of as using the chain rule "backwards."

4. Tangent half-angle substitution - Wikipedia

   en.wikipedia.org/.../Tangent_half-angle_substitution

   The substitution is described in most integral calculus textbooks since the late 19th century, usually without any special name. [5] It is known in Russia as the universal trigonometric substitution , [ 6 ] and also known by variant names such as half-tangent substitution or half-angle substitution .

5. Integral - Wikipedia

   en.wikipedia.org/wiki/Integral

   Integrals also refer to the concept of an antiderivative, a function whose derivative is the given function; in this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides a method to compute the definite integral of a function when its antiderivative is ...

6. Symbolic integration - Wikipedia

   en.wikipedia.org/wiki/Symbolic_integration

   In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e. to find a formula for a differentiable function F(x) such that

7. Wallis' integrals - Wikipedia

   en.wikipedia.org/wiki/Wallis'_integrals

   By means of integration by parts, a reduction formula can be obtained. Using the identity ⁡ = ⁡, we have for all , ⁡ = (⁡) (⁡) = ⁡ ⁡ ⁡. Integrating the second integral by parts, with:

8. Course Hero buys Symbolab in a rare edtech acquisition

   www.aol.com/news/course-hero-buys-symbolab-rare...

   Months after its $80 million Series B fundraise, Course Hero has acquired Symbolab, an artificial intelligence-powered calculator that helps students answer and understand complex math questions.

9. Multiple integral - Wikipedia

   en.wikipedia.org/wiki/Multiple_integral

   Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane which contains its domain. [1]