What is the integral of x(x+2)^4 ?

The integral of x(x+2)^4 is 1/5 x(x+2)^5-1/30 (x+2)^6+C

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integral of x(x+2)^4

\int x (x + 2)^{4} d x

\frac{1}{5} x (x + 2)^{5} - \frac{1}{30} (x + 2)^{6} + C

Solution steps

\int x (x + 2)^{4} d x

Apply Integration By Parts

: \frac{1}{5} x (x + 2)^{5} - \int \frac{1}{5} (x + 2)^{5} d x

= \frac{1}{5} x (x + 2)^{5} - \int \frac{1}{5} (x + 2)^{5} d x

\int \frac{1}{5} (x + 2)^{5} d x = \frac{1}{30} (x + 2)^{6}

= \frac{1}{5} x (x + 2)^{5} - \frac{1}{30} (x + 2)^{6}

Add a constant to the solution

= \frac{1}{5} x (x + 2)^{5} - \frac{1}{30} (x + 2)^{6} + C

f (x) = 4 x^{3} - 12 x^{2}, at x = - 2

\int sin (9 t) d t

\int_{0}^{1} x (\frac{4}{9} x (5 - x^{2})) d x

x \to 3 lim (5 + x)

\frac{\partial}{\partial x} (3 x^{2} - 2 y^{2})

What is the integral of x(x+2)^4 ?
The integral of x(x+2)^4 is 1/5 x(x+2)^5-1/30 (x+2)^6+C