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Generally, if the function is any trigonometric function, and is its derivative, ∫ a cos n x d x = a n sin n x + C {\displaystyle \int a\cos nx\,dx={\frac {a}{n}}\sin nx+C} In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration .
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.
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.
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 .
In integral calculus, the tangent half-angle substitution is a change of variables used for evaluating integrals, which converts a rational function of trigonometric functions of into an ordinary rational function of by setting = .
Sine integral in the complex plane, plotted with a variant of domain coloring. Cosine integral in the complex plane. Note the branch cut along the negative real axis. In mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions.
The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.
4 Trigonometric functions. 5 Rational functions. 6 Exponential function. ... Many books with a list of integrals also have a list of series. This page was ...