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

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

\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

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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