What is the integral of 1/((x+5)^2) ?

The integral of 1/((x+5)^2) is -1/(x+5)+C

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integral of 1/((x+5)^2)

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

- \frac{1}{x + 5} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = x + 5

= - \frac{1}{x + 5}

Add a constant to the solution

= - \frac{1}{x + 5} + C

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

\frac{\partial}{\partial x} (e^{x} ln (y))

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

\frac{d}{d x} (\frac{3 - 4 x}{2})