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

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

Popular >

integral of x(2-x^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{3 x}{4 - x ^{2}} d x

\int + sin (8 x) cos (8 x) d x

\int x π^{x} d x

\int \frac{x ^{3} - 4 x ^{2} + 5}{x - 4} d x

\int (y z^{2} - sin (x) sin (π - y)) d x

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