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

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

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

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

ln x^{2} + 1 + 2 arctan (x) + C

Solution steps

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

Expand

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

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

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

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

= ln x^{2} + 1 + 2 arctan (x)

Add a constant to the solution

= ln x^{2} + 1 + 2 arctan (x) + C

\int \frac{x ^{7} e ^{x} - 8 x ^{6}}{x ^{7}} d x

\frac{d}{d x} (lo g_{18} (x^{2} - 5 x))

\frac{x}{e ^{x} - 1}

\frac{d}{d x} (2 ln (x^{2}))

n = 1 \sum \infty 1 0^{n} x^{n}

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