What is the integral of (3x+2)/(x^2+4) ?

The integral of (3x+2)/(x^2+4) is 3/2 ln|x^2+4|+arctan(x/2)+C

Popular >

integral of (3x+2)/(x^2+4)

\int \frac{3 x + 2}{x ^{2} + 4} d x

\frac{3}{2} ln x^{2} + 4 + arctan (\frac{x}{2}) + C

Solution steps

\int \frac{3 x + 2}{x ^{2} + 4} d x

Expand

\frac{3 x + 2}{x ^{2} + 4} : \frac{3 x}{x ^{2} + 4} + \frac{2}{x ^{2} + 4}

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} + 4} d x + \int \frac{2}{x ^{2} + 4} d x

\int \frac{3 x}{x ^{2} + 4} d x = \frac{3}{2} ln x^{2} + 4

\int \frac{2}{x ^{2} + 4} d x = arctan (\frac{x}{2})

= \frac{3}{2} ln x^{2} + 4 + arctan (\frac{x}{2})

Add a constant to the solution

= \frac{3}{2} ln x^{2} + 4 + arctan (\frac{x}{2}) + C

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

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

\int 3600 - 120 x d x

\int 12 + x - x^{2} d x

\int \frac{t}{cos ^{2} ( t )} d t

What is the integral of (3x+2)/(x^2+4) ?
The integral of (3x+2)/(x^2+4) is 3/2 ln|x^2+4|+arctan(x/2)+C