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

The integral of (1+x^2+1/(1+x^2)) is x+(x^3)/3+arctan(x)+C

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

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

x + \frac{x ^{3}}{3} + arctan (x) + C

Solution steps

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

\int 1 d x = x

\int x^{2} d x = \frac{x ^{3}}{3}

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

= x + \frac{x ^{3}}{3} + arctan (x)

Add a constant to the solution

= x + \frac{x ^{3}}{3} + arctan (x) + C

x \to 2 lim (x^{2} + 3 x + 4)

\int e^{- a x} d x

\frac{d y}{d x} = \frac{8}{7} y

y^{^{''}} + 144 y = sec (12 x)

\frac{1 - 4 ln ( x )}{x ^{5}}

What is the integral of (1+x^2+1/(1+x^2)) ?
The integral of (1+x^2+1/(1+x^2)) is x+(x^3)/3+arctan(x)+C