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

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

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integral of ((x^2+3))/(x^2+1)

\int \frac{( x ^{2} + 3 )}{x ^{2} + 1} d x

2 arctan (x) + x + C

Solution steps

\int \frac{x ^{2} + 3}{x ^{2} + 1} d x

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

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

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

\int 1 d x = x

= 2 arctan (x) + x

Add a constant to the solution

= 2 arctan (x) + x + C

x \to - 2 lim ((3 - x)^{2})

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

(3, 8), (- 7, 7)

\int sin (2 x) e^{c o s (2)} x d x

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

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