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

The integral of (5x-4)^5 is 1/30 (5x-4)^6+C

Popular >

integral of (5x-4)^5

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

\frac{1}{30} (5 x - 4)^{6} + C

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{1}{5} \cdot \frac{u ^{6}}{6}

Substitute back

u = 5 x - 4

= \frac{1}{5} \cdot \frac{( 5 x - 4 ) ^{6}}{6}

Simplify

\frac{1}{5} \cdot \frac{( 5 x - 4 ) ^{6}}{6} : \frac{1}{30} (5 x - 4)^{6}

= \frac{1}{30} (5 x - 4)^{6}

Add a constant to the solution

= \frac{1}{30} (5 x - 4)^{6} + C

\int \frac{1}{ln ( x ^{3} )} d x

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

\int x^{3} - \frac{2}{x ^{2}} + 2 d x

\int \frac{x}{16 - 6 x - x ^{2}} d x

\int (7 x^{2} + x^{- 4}) d x