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For a complete list of integral functions, see lists of integrals. ... Integrals involving s = √ x 2 − a 2. Assume x 2 > a 2 (for x 2 < a 2, see next section):
Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
In the integral , we may use = , = , = . Then, = = () = = = + = +. The above step requires that > and > We can choose to be the principal root of , and impose the restriction / < < / by using the inverse sine function.
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 ...
For a complete list of integral functions, see list of integrals. Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity. Integrals involving only logarithmic functions
3.1 Integrals of hyperbolic tangent, cotangent, secant, cosecant functions 3.2 Integrals involving hyperbolic sine and cosine functions 3.3 Integrals involving hyperbolic and trigonometric functions
For a complete list of integral formulas, see lists of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration. For each inverse hyperbolic integration formula below there is a corresponding formula in the list of integrals of inverse trigonometric functions.