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

The integral of x(x+1)^3 is 1/4 x(x+1)^4-1/20 (x+1)^5+C

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integral of x(x+1)^3

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

\frac{1}{4} x (x + 1)^{4} - \frac{1}{20} (x + 1)^{5} + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{4} x (x + 1)^{4} - \int \frac{1}{4} (x + 1)^{4} d x

= \frac{1}{4} x (x + 1)^{4} - \int \frac{1}{4} (x + 1)^{4} d x

\int \frac{1}{4} (x + 1)^{4} d x = \frac{1}{20} (x + 1)^{5}

= \frac{1}{4} x (x + 1)^{4} - \frac{1}{20} (x + 1)^{5}

Add a constant to the solution

= \frac{1}{4} x (x + 1)^{4} - \frac{1}{20} (x + 1)^{5} + C

\frac{d}{d x} (0.5 e^{x - 1})

x \frac{d y}{d x} + y = x y^{2}

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

\frac{\partial}{\partial x} (3 x - 4 t)

\frac{9}{x - 7}

What is the integral of x(x+1)^3 ?
The integral of x(x+1)^3 is 1/4 x(x+1)^4-1/20 (x+1)^5+C