What is the integral of [5x+2/(3x^5)] ?

The integral of [5x+2/(3x^5)] is (5x^2)/2-1/(6x^4)+C

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integral of [5x+2/(3x^5)]

\int [5 x + \frac{2}{3 x ^{5}}] d x

\frac{5 x ^{2}}{2} - \frac{1}{6 x ^{4}} + C

Solution steps

\int 5 x + \frac{2}{3 x ^{5}} 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 5 x d x + \int \frac{2}{3 x ^{5}} d x

\int 5 x d x = \frac{5 x ^{2}}{2}

\int \frac{2}{3 x ^{5}} d x = - \frac{1}{6 x ^{4}}

= \frac{5 x ^{2}}{2} - \frac{1}{6 x ^{4}}

Add a constant to the solution

= \frac{5 x ^{2}}{2} - \frac{1}{6 x ^{4}} + C

2 a x + \frac{b}{x}

\frac{d}{d x} (arctan (\frac{13}{x}) - arctan (\frac{3}{x}))

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

\frac{d}{d x} (e^{2 x} - x^{2} - 1)

x \to 4 lim (4 - x)

What is the integral of [5x+2/(3x^5)] ?
The integral of [5x+2/(3x^5)] is (5x^2)/2-1/(6x^4)+C