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

The integral from 1 to 2 of 1/((3-5x)^2) is 1/14

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

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

\frac{1}{14}

Decimal Notation

0.07142 \dots

Solution steps

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

Apply u-substitution

: \int_{- 2}^{- 7} - \frac{1}{5 u ^{2}} d u

= \int_{- 2}^{- 7} - \frac{1}{5 u ^{2}} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 7}^{- 2} - \frac{1}{5 u ^{2}} 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_{- 7}^{- 2} \frac{1}{u ^{2}} d u)

Apply the Power Rule

: [- \frac{1}{u}]_{- 7}^{- 2}

= - (- \frac{1}{5} [- \frac{1}{u}]_{- 7}^{- 2})

Simplify

= \frac{1}{5} [- \frac{1}{u}]_{- 7}^{- 2}

Compute the boundaries:

\frac{5}{14}

= \frac{1}{5} \cdot \frac{5}{14}

Simplify

= \frac{1}{14}

π^{x^{2}}

\int \frac{1}{5 - 4 x} d x

\frac{\partial}{\partial b} (\frac{a}{b})

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What is the integral from 1 to 2 of 1/((3-5x)^2) ?
The integral from 1 to 2 of 1/((3-5x)^2) is 1/14