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

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

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integral of x(1+x)^3

integral

x (1 + x)^{3}

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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

\frac{x + 1}{( x )}

\frac{e}{( ( e ) ^{x} ) ^{2}}

\frac{( x - 2 )}{( x - 1 )}

z (1 + i)

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