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

(3 x^{4} - x + 1) (- x^{5} + 4)

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

f (t) = sin (2 t)

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

\frac{d}{d x} (x^{2} + 4 x (\frac{36.5}{x ^{2}}))

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