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

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

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

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

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

Solution steps

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

Simplify

\frac{x ^{2} + 1}{x ^{2} + 1} : \frac{1}{x ^{2} + 1}

= \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

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