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

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

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

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

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

Solution steps

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

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

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

= 2 arctan (x) - \frac{x ^{3}}{3}

Add a constant to the solution

= 2 arctan (x) - \frac{x ^{3}}{3} + C

f (2) = - x^{2} + 6 x - 3

\frac{x}{1 + x ^{2}}, \frac{x ^{2}}{1 + x ^{3}}

\frac{d}{d x} (\frac{1}{4} sin (4 x))

n = 1 \sum \infty (\frac{2}{3})^{n - 1}

x \to o lim (f (x))

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