What is the integral of 1/(sqrt(1+p^2)) ?

The integral of 1/(sqrt(1+p^2)) is ln|sqrt(p^2+1)+p|+C

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integral of 1/(sqrt(1+p^2))

\int \frac{1}{1 + p ^{2}} d p

ln p^{2} + 1 + p + C

Solution steps

\int \frac{1}{1 + p ^{2}} d p

Use the common integral:

\int \frac{1}{1 + p ^{2}} d p = ln p^{2} + 1 + p

= ln p^{2} + 1 + p

Add a constant to the solution

= ln p^{2} + 1 + p + C

What is the integral of 1/(sqrt(1+p^2)) ?
The integral of 1/(sqrt(1+p^2)) is ln|sqrt(p^2+1)+p|+C