What is the integral of (2-x)^3 ?

The integral of (2-x)^3 is -((2-x)^4)/4+C

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integral of (2-x)^3

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

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

Solution steps

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

Apply u-substitution

: \int - u^{3} d u

= \int - u^{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= - \frac{u ^{4}}{4}

Substitute back

u = 2 - x

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

Add a constant to the solution

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

lo g_{10} (x)

\frac{\partial}{\partial y} (y + z)

\frac{d}{d x} ((sin (x))^{3 x})

x \to 0 lim (\frac{sin ( 8 x )}{8})

\frac{1}{2 x - 1}