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

The integral of (1-x)^3 is x-(3x^2)/2+x^3-(x^4)/4+C

Popular >

integral of (1-x)^3

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

x - \frac{3 x ^{2}}{2} + x^{3} - \frac{x ^{4}}{4} + C

Solution steps

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

Expand

(1 - x)^{3} : 1 - 3 x + 3 x^{2} - x^{3}

= \int 1 - 3 x + 3 x^{2} - x^{3} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x - \int 3 x d x + \int 3 x^{2} d x - \int x^{3} d x

\int 1 d x = x

\int 3 x d x = \frac{3 x ^{2}}{2}

\int 3 x^{2} d x = x^{3}

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

= x - \frac{3 x ^{2}}{2} + x^{3} - \frac{x ^{4}}{4}

Add a constant to the solution

= x - \frac{3 x ^{2}}{2} + x^{3} - \frac{x ^{4}}{4} + C

\int_{0}^{1} (4 x) - (4 x) d x

\int \frac{1}{tan ( θ )} d θ

\int 9 \frac{sin ( 2 x )}{sin ( x )} d x

\frac{d}{d x} (\frac{π x}{2})

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

What is the integral of (1-x)^3 ?
The integral of (1-x)^3 is x-(3x^2)/2+x^3-(x^4)/4+C