MHB Integration of hyperbolic function

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The discussion focuses on integrating the function x * sech²(x²) with respect to x. A hint is provided, referencing the derivative of the hyperbolic tangent function, tanh(x), which equals sech²(x). Participants are encouraged to consider the derivative of tanh(x²) to aid in solving the integral. The integration process involves recognizing the relationship between hyperbolic functions and their derivatives. Overall, the conversation emphasizes using known derivatives to simplify the integration task.
paulmdrdo1
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i don't know how start. please help.

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

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

What about

$$\frac{d}{dx} \tanh(x^2)$$
 

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