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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 2 \cdot \int \frac{1}{u ^{3}} d u

Apply the Power Rule

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

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

Substitute back

u = x + 1

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

Simplify

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

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

Add a constant to the solution

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

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

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

\frac{\partial}{\partial x} (x e^{2 t} - 4 x)

x, x - 2, 0

\frac{\partial}{\partial x} (ln (x^{2} - 4 x y + y^{2}))

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