What is the integral of (5-2x)^9 ?

The integral of (5-2x)^9 is -1/20 (5-2x)^{10}+C

integral of (5-2x)^9

\int (5 - 2 x)^{9} d x

- \frac{1}{20} (5 - 2 x)^{10} + C

Solution steps

\int (5 - 2 x)^{9} d x

Apply u-substitution

= \int - \frac{u ^{9}}{2} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int u^{9} d u

Apply the Power Rule

= - \frac{1}{2} \cdot \frac{u ^{10}}{10}

Substitute back

u = 5 - 2 x

= - \frac{1}{2} \cdot \frac{( 5 - 2 x ) ^{10}}{10}

Simplify

- \frac{1}{2} \cdot \frac{( 5 - 2 x ) ^{10}}{10} : - \frac{1}{20} (5 - 2 x)^{10}

= - \frac{1}{20} (5 - 2 x)^{10}

Add a constant to the solution

= - \frac{1}{20} (5 - 2 x)^{10} + C

x \to \infty lim (x sin (\frac{2 π}{x}))

\frac{d}{d x} (12 - 3 x - 4 y)

\int \frac{14}{( 49 x ^{2} + 1 ) ^{2}} d x

d er i v a t i v e f (x) = 2 x^{2} - 9 x + 10

\int x 5 5 - x^{2} d x

What is the integral of (5-2x)^9 ?
The integral of (5-2x)^9 is -1/20 (5-2x)^{10}+C