What is the integral of (-1/(x^2)) ?

The integral of (-1/(x^2)) is 1/x+C

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integral of (-1/(x^2))

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

\frac{1}{x} + C

Solution steps

\int - \frac{1}{x ^{2}} d x

Take the constant out:

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

= - \int \frac{1}{x ^{2}} d x

Apply the Power Rule

: - \frac{1}{x}

= - (- \frac{1}{x})

Simplify

= \frac{1}{x}

Add a constant to the solution

= \frac{1}{x} + C

f (x) = x^{3} + 2, at x = 1

f (x) = sin^{3} (3 x)

y^{^{'}} + 10 y = 4

\int 25 sin^{2} (x) d x

7 x - 7 x