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

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

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integral of (x^2+3)/x

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

\frac{x ^{2}}{2} + 3 ln ∣ x ∣ + C

Solution steps

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

Expand

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

= \int x + \frac{3}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x d x + \int \frac{3}{x} d x

\int x d x = \frac{x ^{2}}{2}

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{x ^{2}}{2} + 3 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} + 3 ln ∣ x ∣ + C

x \to - 2 + lim (\frac{5 x}{2 + x})

f (x) = \frac{1}{20} sin (5 x^{2}) - \frac{1}{4} sin (x^{2})

y = 4 x - 3 x^{2}

f (x) = 3 x^{2} + 2 x - 5, (2, 7)

\int 15 e^{- 31 t} t d t

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