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

The integral from 1 to 2 of 2/((x-5)^3) is -7/144

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

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

- \frac{7}{144}

Decimal

- 0.04861 \dots

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int_{- 4}^{- 3} \frac{1}{u ^{3}} d u

= 2 \cdot \int_{- 4}^{- 3} \frac{1}{u ^{3}} d u

Apply the Power Rule

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

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

Compute the boundaries:

- \frac{7}{288}

= 2 (- \frac{7}{288})

Simplify

= - \frac{7}{144}

\int 4^{x} - \frac{1}{3 x} d x

8 (ln (y)) y^{^{'}} - x^{9} y = 0

\int \frac{3 x ^{5} + 2}{- 5 x ^{5} + 5 x} d x

\frac{d}{d x} (4 e^{x})

\int 2 e^{3} d x

What is the integral from 1 to 2 of 2/((x-5)^3) ?
The integral from 1 to 2 of 2/((x-5)^3) is -7/144