What is Coshx expansion?
Emma Johnson
Updated on February 26, 2026
The expansion of cosh(x) is given below: cosh(x) = 1 + x2/2!
What is the integral of Coshx?
Integrals of Hyperbolic Functions
| Function | Integral |
|---|---|
| coshx | sinhx + c |
| tanhx | ln| coshx | + c |
| cschx | ln| tanh(x/2) | + c |
| sechx | arctan(sinhx) + c = tan-1(sinhx) + c |
What is the expansion of Cos hyperbolic X?
cosh x = ex + e−x 2 . The function satisfies the conditions cosh 0 = 1 and coshx = cosh(−x).
What is cosh and cos?
Hyperbolic Cosine: cosh(x) = ex + e−x 2. (pronounced “cosh”) They use the natural exponential function ex. And are not the same as sin(x) and cos(x), but a little bit similar: sinh vs sin.
What is the derivative of cosh X?
Hyperbolic Functions
| Function | Derivative | Integral |
|---|---|---|
| cosh(x) | sinh(x) | sinh(x) |
| tanh(x) | 1-tanh(x)² | ln(cosh(x)) |
| coth(x) | 1-coth(x)² | ln(|sinh(x)|) |
| sech(x) | -sech(x)*tanh(x) | atan(sinh(x)) |
How do you calculate cosh?
The hyperbolic sine and cosine are given by the following: cosh a = e a + e − a 2 , sinh a = e a − e − a 2 .
What is the antiderivative of sec(x)?
The antiderivative of sec(x) is equal to ln |sec(x) + tan(x)| + C, where C represents a constant. This antiderivative, also known as an integral, can be solved by using the integration technique known as substitution.
What is the integral of cos2x?
The integral of cos(2x) is 1/2 x sin(2x) + C, where C is equal to a constant. The integral of the function cos(2x) can be determined by using the integration technique known as substitution. In calculus, substitution is derived from the chain rule for differentiation.
What is integral tan x?
The integral of tan(x) is -ln |cos x| + C. In this equation, ln indicates the function for a natural logarithm, while cos is the function cosine, and C is a constant.
What is the application of integral calculus?
Applications of integral calculus include computations involving area, volume, arc length, center of mass, work, and pressure. More advanced applications include power series and Fourier series . Calculus is also used to gain a more precise understanding of the nature of space, time, and motion.
