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

The integral of (2+x^2)/(1+x^2) is arctan(x)+x+C

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

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

arctan (x) + x + C

Solution steps

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

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

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int 1 d x = x

= arctan (x) + x

Add a constant to the solution

= arctan (x) + x + C

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

\frac{\partial}{\partial x} (\frac{( 2 x y )}{x ^{2} + y ^{2}})

\frac{d}{d x} (\frac{2 - x}{( 3 - x ) ^{4}})

\frac{d}{d x} (5 x e^{- x})

\int_{- 4}^{- 1} - \frac{4}{x ^{3}} d x

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