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Popular >

integral of 5/(x^3)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= 5 \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

: - \frac{1}{2 x ^{2}}

= 5 (- \frac{1}{2 x ^{2}})

Simplify

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

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

Add a constant to the solution

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

Popular Examples

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\int \frac{cos ( 3 x ) + 3}{sin ( 3 x )} d x

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\frac{3}{s ( s + 3 ) + 6}

(\partial)/(\partial x)(|x|y)

\frac{\partial}{\partial x} (∣ x ∣ y)

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

\frac{d}{d x} (\frac{e ^{3 x} + e ^{x^{2}}}{3})

integral of e^{-3x}+2x

\int e^{- 3 x} + 2 x d x

Frequently Asked Questions (FAQ)

What is the integral of 5/(x^3) ?
The integral of 5/(x^3) is -5/(2x^2)+C