What is the integral of (x-17)/(x^2+1) ?

The integral of (x-17)/(x^2+1) is 1/2 ln|x^2+1|-17arctan(x)+C

Popular >

integral of (x-17)/(x^2+1)

\int \frac{x - 17}{x ^{2} + 1} d x

\frac{1}{2} ln x^{2} + 1 - 17 arctan (x) + C

Solution steps

\int \frac{x - 17}{x ^{2} + 1} d x

Expand

\frac{x - 17}{x ^{2} + 1} : \frac{x}{x ^{2} + 1} - \frac{17}{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{x}{x ^{2} + 1} d x - \int \frac{17}{x ^{2} + 1} d x

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

\int \frac{17}{x ^{2} + 1} d x = 17 arctan (x)

= \frac{1}{2} ln x^{2} + 1 - 17 arctan (x)

Add a constant to the solution

= \frac{1}{2} ln x^{2} + 1 - 17 arctan (x) + C

\frac{\partial}{\partial x} (x^{2} sin (3 x y))

\int sin (3 x + 1) d x

\frac{\partial}{\partial x} (5 cos (2 x + 5 y))

\int \frac{5 x ^{3}}{6 + x ^{2}} d x

\frac{d}{d x} (2 sin (2 x))

What is the integral of (x-17)/(x^2+1) ?
The integral of (x-17)/(x^2+1) is 1/2 ln|x^2+1|-17arctan(x)+C