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

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

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

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

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

Solution steps

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

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

Add a constant to the solution

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

y^{^{''}} + 2 y = sin (2 x)

\frac{d}{d x} (\frac{x ^{4} - 3 x ^{2} + 1}{( 2 x + 3 ) ^{4}})

\frac{d}{d x} (\frac{2 x}{2})

4 x^{2} + 16 y^{2} - 51

\frac{\partial}{\partial x} (ln e^{1 + x^{2}} + 3 x^{4} + cot^{2} (π x))

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