What is the integral of (6x^5-5/(x^5)) ?

The integral of (6x^5-5/(x^5)) is x^6+5/(4x^4)+C

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integral of (6x^5-5/(x^5))

\int (6 x^{5} - \frac{5}{x ^{5}}) d x

x^{6} + \frac{5}{4 x ^{4}} + C

Solution steps

\int 6 x^{5} - \frac{5}{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 6 x^{5} d x - \int \frac{5}{x ^{5}} d x

\int 6 x^{5} d x = x^{6}

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

= x^{6} - (- \frac{5}{4 x ^{4}})

Simplify

= x^{6} + \frac{5}{4 x ^{4}}

Add a constant to the solution

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

\frac{d y}{d x} = \frac{e ^{x}}{9 + e ^{x}}

(1 + x) y^{^{'}} = (x + 2) (y - 1)

x \to \frac{x}{6} lim (cot (x))

y = x^{2} + 5 x

16 x, \frac{4}{x}, \frac{1}{4} x

What is the integral of (6x^5-5/(x^5)) ?
The integral of (6x^5-5/(x^5)) is x^6+5/(4x^4)+C