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Popular >

integral of x^3(1-x)

Solution

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

Solution

\frac{x ^{4}}{4} - \frac{x ^{5}}{5} + C

Solution steps

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

Expand

x^{3} (1 - x) : x^{3} - x^{4}

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

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

\int x^{4} d x = \frac{x ^{5}}{5}

= \frac{x ^{4}}{4} - \frac{x ^{5}}{5}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{x ^{5}}{5} + C

Popular Examples

integral of cos(x/4)

\int cos (\frac{x}{4}) d x

integral of-x^2-4

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

(\partial)/(\partial x)(sin^3(x))

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

(x^{7})^{^{'}}

integral of 1/(x*ln(2x))

\int \frac{1}{x \cdot ln ( 2 x )} d x

Frequently Asked Questions (FAQ)

What is the integral of x^3(1-x) ?
The integral of x^3(1-x) is (x^4)/4-(x^5)/5+C