What is the integral of (3/(x^3)) ?

The integral of (3/(x^3)) is -3/(2x^2)+C

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integral of (3/(x^3))

\int (\frac{3}{x ^{3}}) d x

- \frac{3}{2 x ^{2}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= 3 (- \frac{1}{2 x ^{2}})

Simplify

3 (- \frac{1}{2 x ^{2}}) : - \frac{3}{2 x ^{2}}

= - \frac{3}{2 x ^{2}}

Add a constant to the solution

= - \frac{3}{2 x ^{2}} + C

\frac{d}{d t} (e^{i t})

\frac{d x}{d t} = sin (2 π (t + 3))

1

n = 3 \sum \infty \frac{1}{3} (\frac{2}{5})^{n}