Question
Use numerical methods or a calculator to -approximate the following integrals as closely as possible.$$\int_{0}^{\infty} \ln \left(\frac{e^{x}+1}{e^{x}-1}\right) d x=\frac{\pi^{2}}{4}$$
Step 1
The integral is an improper integral from 0 to infinity of the natural logarithm of the function $\frac{e^{x}+1}{e^{x}-1}$. Show more…
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Use numerical methods or a calculator to approximate the following integrals as closely as possible. The exact value of each integral is given. $$\int_{0}^{\infty} \ln \left(\frac{e^{x}+1}{e^{x}-1}\right) d x=\frac{\pi^{2}}{4}$$
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