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

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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

y = x^{3} - 7 x, y = 9 x

\frac{t}{5}

y^{^{'}} - 6 y = x

\int_{2}^{\infty} e^{- 6 p} d p

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