What is the integral from 1 to 2 of (2x-5)^3 ?

The integral from 1 to 2 of (2x-5)^3 is -10

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integral from 1 to 2 of (2x-5)^3

\int_{1}^{2} (2 x - 5)^{3} d x

- 10

Solution steps

\int_{1}^{2} (2 x - 5)^{3} d x

Apply u-substitution

: \int_{- 3}^{- 1} \frac{u ^{3}}{2} d u

= \int_{- 3}^{- 1} \frac{u ^{3}}{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_{- 3}^{- 1} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{- 3}^{- 1}

= \frac{1}{2} [\frac{u ^{4}}{4}]_{- 3}^{- 1}

Compute the boundaries:

- 20

= \frac{1}{2} (- 20)

Simplify

= - 10

\frac{d}{d x} ((\frac{x + 2}{x - 2})^{2})

\int (x - x + 1) (x + 1) d x

12 x^{3} - 3 y^{2} x^{4} + 1 \frac{d y}{d x} = 0

\frac{\partial}{\partial x} (cos^{5} (x^{3} y^{8}))

\frac{d ^{2} y}{d x ^{2}} = - y

What is the integral from 1 to 2 of (2x-5)^3 ?
The integral from 1 to 2 of (2x-5)^3 is -10