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

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

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

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

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

Solution steps

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

Simplify

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

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

Use the common integral:

\int \frac{1}{1 + x ^{2}} 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(1+x^2))/(1+x^2) ?
The integral of (sqrt(1+x^2))/(1+x^2) is ln|sqrt(x^2+1)+x|+C