What is the integral of (x+2)^{-2} ?

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

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integral of (x+2)^{-2}

\int (x + 2)^{- 2} d x

- \frac{1}{x + 2} + C

Solution steps

\int (x + 2)^{- 2} d x

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

= - \frac{1}{x + 2}

Add a constant to the solution

= - \frac{1}{x + 2} + C

\int \frac{6 ( x ^{2} + 5 )}{x ( x ^{2} + 6 )} d x

\frac{1}{3} x^{\frac{3}{2}}

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10 \frac{e ^{- 3 s}}{s}