Power in a power integral?

Calculus Level 4

∫ − 1 1 ( e x 2 e x + 1 + 2 x e x 2 ln ⁡ ( e x + 1 ) ) d x = ? \large{\int_{-1}^{1} \left( \dfrac{e^{x^2}}{e^x +1} + 2xe^{x^2} \ln(e^x+1) \right) \, dx = \, ?}

Give your answer to 3 decimal places.


The answer is 2.718.

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Satyajit Mohanty by Satyajit Mohanty , 24, India

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Please edit the integral dude :)
This problem can be attacked by using product rule in differentiation

e**(x**2) ln( e**x + 1 )

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nope. This is wrong. Try differentiating again.

Pi Han Goh - 5 years, 6 months ago

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This is not wrong. When you apply the property of definite integral f(x)=f(a+b-x). (you know what im talking about.) the e^x which was missing will come in the numerator of the first term. Then you can apply u substitution as vincent miller suggested. And the answer will come out as e(ln(e))=e

Arghyadeep Chatterjee - 3 years, 1 month ago

Integration from -a to a results as f(a)+f(-a) from 0 to a then it can be integrated by basic formulae

Rupayan Jana - 2 years ago

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