What is the integral of (5-3x)^7 ?

The integral of (5-3x)^7 is -1/24 (5-3x)^8+C

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integral of (5-3x)^7

\int (5 - 3 x)^{7} d x

- \frac{1}{24} (5 - 3 x)^{8} + C

Solution steps

\int (5 - 3 x)^{7} d x

Apply u-substitution

: \int - \frac{u ^{7}}{3} d u

= \int - \frac{u ^{7}}{3} d u

Take the constant out:

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

= - \frac{1}{3} \cdot \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= - \frac{1}{3} \cdot \frac{u ^{8}}{8}

Substitute back

u = 5 - 3 x

= - \frac{1}{3} \cdot \frac{( 5 - 3 x ) ^{8}}{8}

Simplify

- \frac{1}{3} \cdot \frac{( 5 - 3 x ) ^{8}}{8} : - \frac{1}{24} (5 - 3 x)^{8}

= - \frac{1}{24} (5 - 3 x)^{8}

Add a constant to the solution

= - \frac{1}{24} (5 - 3 x)^{8} + C

\int 2 x^{- 5} d x

\frac{\partial}{\partial y} (5 y - e^{8 s i n (x)})

n = 6 \sum \infty \frac{1}{n ^{2} - 4}

n = 1 \sum \infty \frac{1}{n ^{- 10}}

y = x^{2} + x + 3