Integral of sec 3x

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The integral of secant cubed is a frequent and challenging [1] indefinite integral of elementary calculus :. This antiderivative may be found by integration by parts , as follows: [2]. This admits a decomposition by partial fractions :. Just as the integration by parts above reduced the integral of secant cubed to the integral of secant to the first power, so a similar process reduces the integral of higher odd powers of secant to lower ones. This is the secant reduction formula, which follows the syntax:. Even powers of tangents can be accommodated by using binomial expansion to form an odd polynomial of secant and using these formulae on the largest term and combining like terms. Contents move to sidebar hide.

Integral of sec 3x

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Contents move to sidebar hide. Rolle's theorem Mean value theorem Inverse function theorem. Antiderivative Integral improper Riemann integral Lebesgue integration Contour integration Integral of inverse functions.

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It can be calculated using the substitution method. Integration is the reverse process of differentiation, hence determining the integration of sec 3x is the same as finding the antiderivative of sec 3x. Further in this article, we will evaluate the integration of sec 3x step-wise using the substitution method. We will also find the integration of sec 3x combined with different functions and solve a few examples for a better understanding. The integration of sec 3x is the process of finding the antiderivative of sec 3x. We can calculate the integration of sec 3x using the substitution method by substituting 3x with another variable and solving the integral. Let now go through the formula for the integral of sec 3x.

Integral of sec 3x

Integral of sec cube x along with its formula and proof with examples. In calculus , the integral is a fundamental concept that assigns numbers to functions to define displacement, area, volume, and all those functions that contain a combination of tiny elements. It is categorized into two parts, definite integral and indefinite integral. The process of integration calculates the integrals. This process is defined as finding an antiderivative of a function. Integrals can handle almost all functions, such as trigonometric, algebraic, exponential, logarithmic, etc. This article will teach you what is integral to a trigonometric function cubic sec x. You will also understand how to compute sec cube integral by using different integration techniques.

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Antiderivative Integral improper Riemann integral Lebesgue integration Contour integration Integral of inverse functions. Read Edit View history. Subscription plan. Fractional Malliavin Stochastic Variations. Hidden categories: Articles with short description Short description matches Wikidata Pages using sidebar with the child parameter. Just as the integration by parts above reduced the integral of secant cubed to the integral of secant to the first power, so a similar process reduces the integral of higher odd powers of secant to lower ones. Read more. Toggle limited content width. No ads. This admits a decomposition by partial fractions :. Calculus on Euclidean space Generalized functions Limit of distributions.

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Differentiation notation Second derivative Implicit differentiation Logarithmic differentiation Related rates Taylor's theorem. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. This antiderivative may be found by integration by parts , as follows: [2]. Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral improper Riemann integral Lebesgue integration Contour integration Integral of inverse functions Integration by Parts Discs Cylindrical shells Substitution trigonometric , tangent half-angle , Euler Euler's formula Partial fractions Changing order Reduction formulae Differentiating under the integral sign Risch algorithm. Category : Integral calculus. Parts Discs Cylindrical shells Substitution trigonometric , tangent half-angle , Euler Euler's formula Partial fractions Changing order Reduction formulae Differentiating under the integral sign Risch algorithm. Differentiation rules List of integrals of exponential functions List of integrals of hyperbolic functions List of integrals of inverse hyperbolic functions List of integrals of inverse trigonometric functions List of integrals of irrational functions List of integrals of logarithmic functions List of integrals of rational functions List of integrals of trigonometric functions Secant Secant cubed List of limits Lists of integrals. Even powers of tangents can be accommodated by using binomial expansion to form an odd polynomial of secant and using these formulae on the largest term and combining like terms. Antiderivative Arc length Riemann integral Basic properties Constant of integration Fundamental theorem of calculus Differentiating under the integral sign Integration by parts Integration by substitution trigonometric Euler Tangent half-angle substitution Partial fractions in integration Quadratic integral Trapezoidal rule Volumes Washer method Shell method Integral equation Integro-differential equation. Calculus - Early Transcendentals. No ads. Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Integral Lists of integrals Integral transform Leibniz integral rule.