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

The integral of (5x-3)^4 is 1/25 (5x-3)^5+C

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integral of (5x-3)^4

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

\frac{1}{25} (5 x - 3)^{5} + C

Solution steps

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

Apply u-substitution

: \int \frac{u ^{4}}{5} d u

= \int \frac{u ^{4}}{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^{4} d u

Apply the Power Rule

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

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

Substitute back

u = 5 x - 3

= \frac{1}{5} \cdot \frac{( 5 x - 3 ) ^{5}}{5}

Simplify

\frac{1}{5} \cdot \frac{( 5 x - 3 ) ^{5}}{5} : \frac{1}{25} (5 x - 3)^{5}

= \frac{1}{25} (5 x - 3)^{5}

Add a constant to the solution

= \frac{1}{25} (5 x - 3)^{5} + C

y = \frac{x ^{2}}{3} + x + \frac{1}{2}

\frac{90}{x}

\int_{0}^{2} \frac{x}{( 1 + x ^{2} ) ^{2}} d x

\frac{d}{d x} ((5 - 6 x)^{5})

2 x + \frac{3}{x}