What is the integral of (5x-1)^3 ?

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

integral of (5x-1)^3

\int (5 x - 1)^{3} d x

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

Solution steps

\int (5 x - 1)^{3} d x

Apply u-substitution

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

Substitute back

u = 5 x - 1

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

Simplify

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

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

Add a constant to the solution

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

t an g e n t \frac{3 x ^{2}}{( 3 - 2 x ) ^{4}}

\int (2 t e^{t}) d t

t an g e n t y^{4} - 4 y^{2} = x^{4} - 9 x^{2}, (- 3, 2)

d er i v a t i v e y = e^{4 x} cos (7 x)

d er i v a t i v e 4 x ln (x)