What is the integral of x(1-4x^2) ?

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

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integral of x(1-4x^2)

\int x (1 - 4 x^{2}) d x

\frac{1}{2} x^{2} - x^{4} + C

Solution steps

\int x (1 - 4 x^{2}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} (1 - 4 x^{2}) - \int - 4 x^{3} d x

= \frac{1}{2} x^{2} (1 - 4 x^{2}) - \int - 4 x^{3} d x

\int - 4 x^{3} d x = - x^{4}

= \frac{1}{2} x^{2} (1 - 4 x^{2}) - (- x^{4})

Simplify

\frac{1}{2} x^{2} (1 - 4 x^{2}) - (- x^{4}) : \frac{1}{2} x^{2} - x^{4}

= \frac{1}{2} x^{2} - x^{4}

Add a constant to the solution

= \frac{1}{2} x^{2} - x^{4} + C

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