# How do you integrate #ln(x+sqrt(x^2+1))#?

By parts.

You can integrate it by parts with the rule

where we assume that

consequently

The integral is then

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To integrate ln(x+sqrt(x^2+1)), you can use integration by parts. Let u = ln(x + sqrt(x^2 + 1)) and dv = dx. Then, differentiate u to find du, and integrate dv to find v. After that, use the integration by parts formula:

∫udv = uv - ∫vdu

Finally, substitute the values of u, v, du, and dv into the formula and solve for the integral.

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