How calcule this integral: x*e^x^2/e^x^2 + 1?

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The integral in question is x*e^(x^2)/(e^(x^2) + 1). A suggested substitution is u = e^(x^2) + 1, which leads to the need for calculating du. The derivative of e^(f(x)) is f'(x) * e^(f(x)), which is relevant for finding du. The discussion emphasizes the importance of showing effort in solving the integral and clarifying the steps after the u-substitution. Understanding these concepts is crucial for successfully calculating the integral.
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How calcule this integral: x*e^x^2/e^x^2 + 1

Please help me.
 
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Father20 said:
How calcule this integral: x*e^x^2/e^x^2 + 1

Please help me.

Let u=e^{x^2}+1
 
and further? Thank you for your help.
 
You need to show some effort. What do you do after making a u-substitution?
 
du= e^x^2 dx normally.
 
Not quite.

\frac{d}{dx}e^{f(x)}=f'(x)\cdot e^{f(x)}
 
But after this, what's then. Sorry for my questions.
 
Well first, apply the rule I just showed you. What does du equal?
 

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