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

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

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

integral

\frac{( x ^{4} + 3 )}{x}

\frac{x ^{4}}{4} + 3 ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

\int x^{3} d x = \frac{x ^{4}}{4}

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{x ^{4}}{4} + 3 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{4}}{4} + 3 ln ∣ x ∣ + C

- 5 x + 3

\frac{( e ^{- x} ) ^{2}}{y}

(x^{2} - 5 x) e^{x}

\frac{( x + 3 )}{( x ^{2} + 3 )}

\frac{1}{cos ^{2} ( y )}

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