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Popular >

integral of x+4-4/x

Solution

\int x + 4 - \frac{4}{x} d x

Solution

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

Solution steps

\int x + 4 - \frac{4}{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 4 d x - \int \frac{4}{x} d x

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

\int 4 d x = 4 x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= \frac{x ^{2}}{2} + 4 x - 4 ln ∣ x ∣

Add a constant to the solution

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

Popular Examples

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derivative of (x^{3/2}-4x(x^4-3/(x^2)+2))

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derivative of sqrt(4x+2)derivative of

4 x + 2

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\frac{d}{d x} (\frac{2 x ^{2} + 5 x + 8}{2 x ^{2}})

Frequently Asked Questions (FAQ)

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