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Popular >

integral of x^4-2/x

Solution

\int x^{4} - \frac{2}{x} d x

Solution

\frac{x ^{5}}{5} - 2 ln ∣ x ∣ + C

Solution steps

\int x^{4} - \frac{2}{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^{4} d x - \int \frac{2}{x} d x

\int x^{4} d x = \frac{x ^{5}}{5}

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{x ^{5}}{5} - 2 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{5}}{5} - 2 ln ∣ x ∣ + C

Popular Examples

(\partial)/(\partial x)((x+y)ln(xy))

\frac{\partial}{\partial x} ((x + y) ln (x y))

limit as x approaches 0 of 4/(x^5)

x \to 0 lim (\frac{4}{x ^{5}})

derivative of x^2sin(x)

\frac{d}{d x} (x^{2} sin (x))

derivative of e^{ktan(sqrt(7x)})

\frac{d}{d x} (e^{k t a n (7 x)})

tangent of 5-x-x^2 tangent of

5 - x - x^{2}

Frequently Asked Questions (FAQ)

What is the integral of x^4-2/x ?
The integral of x^4-2/x is (x^5)/5-2ln|x|+C