What is the integral of 5(1-x)^4 ?

The integral of 5(1-x)^4 is -(1-x)^5+C

Popular >

integral of 5(1-x)^4

\int 5 (1 - x)^{4} d x

- (1 - x)^{5} + C

Solution steps

\int 5 (1 - x)^{4} d x

Take the constant out:

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

= 5 \cdot \int (1 - x)^{4} d x

Apply u-substitution

: \int - u^{4} d u

= 5 \cdot \int - u^{4} d u

Take the constant out:

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

= 5 (- \int u^{4} d u)

Apply the Power Rule

: \frac{u ^{5}}{5}

= 5 (- \frac{u ^{5}}{5})

Substitute back

u = 1 - x

= 5 (- \frac{( 1 - x ) ^{5}}{5})

Simplify

5 (- \frac{( 1 - x ) ^{5}}{5}) : - (1 - x)^{5}

= - (1 - x)^{5}

Add a constant to the solution

= - (1 - x)^{5} + C

\int \frac{24}{x ^{3}} d x

x \to 1 lim (\frac{x - 3}{x ^{2} + 4})

\frac{d y}{d x} = x + y, y (0) = 3

\frac{2}{65 + 4 t}

(x^{2} + y^{2}) d x = x y d y