Integration of hyperbolic function

MHB
Thread starter paulmdrdo1
Start date Sep 30, 2013
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Function Hyperbolic Integration

In summary, hyperbolic functions are a set of mathematical functions that are related to the hyperbola and can be defined in terms of exponential functions. They can be integrated using standard techniques and have various applications in physics, engineering, and other fields. Their symmetry and identities aid in simplifying integrals.

Sep 30, 2013

paulmdrdo1

i don't know how start. please help.

$\displaystyle\int xsech^2(x^2)dx$

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Sep 30, 2013

alyafey22

Gold Member

MHB

Hint :

$\displaystyle \frac{d}{dx} \tanh(x)=\text{sech}^2(x)$

What about

$\displaystyle \frac{d}{dx} \tanh(x^2)$

1. What are hyperbolic functions?

Hyperbolic functions are a set of mathematical functions that are related to the hyperbola. They are analogous to the trigonometric functions and can be defined in terms of exponential functions.

2. How are hyperbolic functions integrated?

Hyperbolic functions can be integrated using standard integration techniques, such as substitution or integration by parts. The resulting integrals may involve hyperbolic functions, logarithmic functions, or inverse hyperbolic functions.

3. What is the purpose of integrating hyperbolic functions?

Integrating hyperbolic functions allows us to solve various mathematical problems, such as finding the area under a hyperbolic curve or determining the volume of a solid of revolution with a hyperbolic cross-section.

4. Are there any special properties of hyperbolic functions that aid in integration?

One notable property of hyperbolic functions is their symmetry, which can be used to simplify integrals. Additionally, hyperbolic functions have identities that can be used to transform integrals into more manageable forms.

5. Can hyperbolic functions be used in real-world applications?

Yes, hyperbolic functions have many applications in physics, engineering, and other fields. They can be used to model various physical phenomena, such as the shape of a hanging chain or the motion of a mass attached to a spring.