What is the integral of (5x-4)^3 ?

The integral of (5x-4)^3 is 1/20 (5x-4)^4+C

Popular >

integral of (5x-4)^3

\int (5 x - 4)^{3} d x

\frac{1}{20} (5 x - 4)^{4} + C

Solution steps

\int (5 x - 4)^{3} d x

Apply u-substitution

: \int \frac{u ^{3}}{5} d u

= \int \frac{u ^{3}}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int u^{3} d u

Apply the Power Rule

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

= \frac{1}{5} \cdot \frac{u ^{4}}{4}

Substitute back

u = 5 x - 4

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

Simplify

\frac{1}{5} \cdot \frac{( 5 x - 4 ) ^{4}}{4} : \frac{1}{20} (5 x - 4)^{4}

= \frac{1}{20} (5 x - 4)^{4}

Add a constant to the solution

= \frac{1}{20} (5 x - 4)^{4} + C

\frac{d}{d x} (\frac{\frac{d}{d x} ( 2 )}{x})

\frac{d}{d x} (x e^{y}) = \frac{d}{d x} (x - y)

y = 4 e^{x} + 4 ln (x)

\int \frac{sin ( a x )}{c + cos ( a x )} d x

\frac{d}{d x} (100 x y)