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Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Type in any integral to get the solution, steps and graph.
- Definite Integrals
Free definite integral calculator - solve definite integrals...
- Definite Integrals
The Integral Calculator lets you calculate integrals and antiderivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. It helps you practice by showing you the full working (step by step integration).
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The integral of the secant function defines the Lambertian function, which is the inverse of the Gudermannian function: ∫ 0 φ sec t d t = lam φ = gd − 1 φ . {\displaystyle \int _{0}^{\varphi }\sec t\,dt=\operatorname {lam} \varphi =\operatorname {gd} ^{-1}\varphi .}
21 Σεπ 2013 · The point is to convert this trigonometric integral into the integral of a rational function, integrate that with partial fractions, and then convert back. We use the substitution u = tan(x / 2), for which sinx = 2u 1 + u2, cosx = 1 − u2 1 + u2, dx = 2du 1 + u2.
What we need to do is add together the formulas for the derivatives of the secant and tangent functions. Notice that sec x + tan x appears on both sides of the equation here. If we let u = sec x + tan x and substitute, our equation becomes: u = u · sec x. sec x = . = ln(u).
2 Οκτ 2018 · The integral formula for secant is often introduced in a very artificial way. In this post, I look at the history of this integral and give several derivations.
