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

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

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

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

4 ln ∣ x ∣ + 3 x + \frac{x ^{4}}{2} + C

Solution steps

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

Expand

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

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int 3 d x = 3 x

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

= 4 ln ∣ x ∣ + 3 x + \frac{x ^{4}}{2}

Add a constant to the solution

= 4 ln ∣ x ∣ + 3 x + \frac{x ^{4}}{2} + C

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