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

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

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

\int \frac{1}{( x ^{2} + 1 )} d x

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

Solution steps

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

Use the common integral:

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

= ln x^{2} + 1 + x

Add a constant to the solution

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

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