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

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

Popular >

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

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

- \frac{x ^{2}}{2 ( x + 3 ) ^{2}} + ln ∣ x + 3 ∣ + \frac{3}{x + 3} + C

Solution steps

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

Apply Integration By Parts

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

\int - \frac{x}{( x + 3 ) ^{2}} d x = - ln ∣ x + 3 ∣ - \frac{3}{x + 3}

= - \frac{x ^{2}}{2 ( x + 3 ) ^{2}} - (- ln ∣ x + 3 ∣ - \frac{3}{x + 3})

Simplify

= - \frac{x ^{2}}{2 ( x + 3 ) ^{2}} + ln ∣ x + 3 ∣ + \frac{3}{x + 3}

Add a constant to the solution

= - \frac{x ^{2}}{2 ( x + 3 ) ^{2}} + ln ∣ x + 3 ∣ + \frac{3}{x + 3} + C

\int 6 x^{4} d x

\frac{d v}{d t} + \frac{( v ^{^{'}} \cdot v )}{t} = v^{^{'}} \cdot (\frac{t}{2} - \frac{1}{2})

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

x \to 0 lim (3 x^{2} + 2 x h + h^{2})

\frac{\partial}{\partial x} (9 - x^{2} - y)

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