What is the integral of (10)/(x^5) ?

The integral of (10)/(x^5) is -5/(2x^4)+C

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integral of (10)/(x^5)

\int \frac{10}{x ^{5}} d x

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

Solution steps

\int \frac{10}{x ^{5}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int \frac{1}{x ^{5}} d x

Apply the Power Rule

: - \frac{1}{4 x ^{4}}

= 10 (- \frac{1}{4 x ^{4}})

Simplify

10 (- \frac{1}{4 x ^{4}}) : - \frac{5}{2 x ^{4}}

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

Add a constant to the solution

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

t y^{^{'}} + 2 y = \frac{2}{1 + t ^{2}}

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{x} sin (2 x)

\frac{\partial}{\partial x} (arctan (2 x y))

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