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Popular >

integral of a/(x^3)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

sum from n=1 to infinity of 1^n

n = 1 \sum \infty 1^{n}

integral of 2ax

\int 2 a x d x

limit as x approaches 0 of (x+1)^{1/x}

x \to 0 lim ((x + 1)^{\frac{1}{x}})

x^3y^{'''}-x^2y^{''}+2xy^'-2y=0

x^{3} y^{^{'''}} - x^{2} y^{^{''}} + 2 x y^{^{'}} - 2 y = 0

limit as x approaches-infinity of e^{3x}(2-x)

x \to - \infty lim (e^{3 x} (2 - x))

Frequently Asked Questions (FAQ)

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