What is the integral of 1/((x+2)^3) ?

The integral of 1/((x+2)^3) is -1/(2(x+2)^2)+C

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integral of 1/((x+2)^3)

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

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

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

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

= - \frac{1}{2 u ^{2}}

Substitute back

u = x + 2

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

Add a constant to the solution

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

f (x) = \frac{x}{x + 3}

\frac{\partial}{\partial x} (e^{ik x})

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

\frac{d}{d x} (ln ((x - 4)^{3}))

\int x \cdot x^{2} + 5 d x

What is the integral of 1/((x+2)^3) ?
The integral of 1/((x+2)^3) is -1/(2(x+2)^2)+C