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paulmdrdo1
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i don't know how start. please help.
$\displaystyle\int xsech^2(x^2)dx$
$\displaystyle\int xsech^2(x^2)dx$
Integration of hyperbolic function
- Context: MHB
- Thread starter paulmdrdo1
- Start date
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SUMMARY
The discussion focuses on the integration of the hyperbolic function, specifically the integral $\displaystyle\int x \text{sech}^2(x^2)dx$. A key hint provided is the derivative of the hyperbolic tangent function, $\frac{d}{dx} \tanh(x) = \text{sech}^2(x)$. Additionally, the derivative of $\tanh(x^2)$ is questioned, indicating a need for understanding the chain rule in differentiation of hyperbolic functions.
PREREQUISITES- Understanding of hyperbolic functions, specifically $\tanh(x)$ and $\text{sech}(x)$.
- Knowledge of integration techniques involving substitution.
- Familiarity with differentiation rules, particularly the chain rule.
- Basic calculus concepts, including integrals and derivatives.
- Study the integration techniques for hyperbolic functions.
- Learn about the chain rule in differentiation, specifically for composite functions.
- Explore the properties and applications of hyperbolic functions in calculus.
- Practice solving integrals involving hyperbolic functions with varying degrees of complexity.
Students and professionals in mathematics, particularly those studying calculus and integration techniques involving hyperbolic functions.
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