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

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

Popular >

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

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

\frac{3}{2} ln x^{2} + 1 - 2 arctan (x) + C

Solution steps

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

Expand

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

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

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

= \frac{3}{2} ln x^{2} + 1 - 2 arctan (x)

Add a constant to the solution

= \frac{3}{2} ln x^{2} + 1 - 2 arctan (x) + C

e^{u}

\int \frac{x}{4 x ^{2} - 5} d x

\int \frac{cos ( 4 ln ( x ) )}{x} d x

\int \frac{1}{9} cos (θ) d θ

\int (2 x^{4} + 30 e^{5 x} + x + 8) d x

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