What is the integral of (x^2+16)/x ?

The integral of (x^2+16)/x is (x^2)/2+16ln|x|+C

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integral of (x^2+16)/x

\int \frac{x ^{2} + 16}{x} d x

\frac{x ^{2}}{2} + 16 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{2} + 16}{x} d x

Expand

\frac{x ^{2} + 16}{x} : x + \frac{16}{x}

= \int x + \frac{16}{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{16}{x} d x

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

\int \frac{16}{x} d x = 16 ln ∣ x ∣

= \frac{x ^{2}}{2} + 16 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} + 16 ln ∣ x ∣ + C

\int_{0}^{2 π} 5 cos (x) d x

y^{^{'}} = \frac{y \cdot ln ( x )}{x \cdot ln ( y )}

n = 1 \sum \infty \frac{x ^{n}}{9 ^{n}}

\frac{d y}{d t} + 2 y = 3 \cdot sin (6 t)

x \to - 2 - lim (\frac{- 1}{x ^{2} - 4})

What is the integral of (x^2+16)/x ?
The integral of (x^2+16)/x is (x^2)/2+16ln|x|+C