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

f (x) = \frac{( x + 1 ) ^{2}}{1 + x ^{2}}

\int_{1}^{4} (1 - u) u d u

\frac{3 x}{4 - x ^{2}} = y, at x = 1

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

\int \frac{1}{x ^{2} + 4 x + 5} d x