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

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

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

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

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

Solution steps

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

Use the common integral:

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

= ln v^{2} + 1 + v

Add a constant to the solution

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

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