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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

9 y^{^{''}} - 12 y^{^{'}} + 4 y = e^{- 3 x}

\int \frac{e ^{x}}{e ^{x} + e ^{2 x} - 2} d x

\frac{d}{d x} (x^{2} + 8)

(x + y) d x + x ln (x) d y = 0

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

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