What is the integral from 5 to 10 of 2/((x+2)^2) ?

The integral from 5 to 10 of 2/((x+2)^2) is 5/42

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integral from 5 to 10 of 2/((x+2)^2)

\int_{5}^{10} \frac{2}{( x + 2 ) ^{2}} d x

\frac{5}{42}

Decimal

0.11904 \dots

Solution steps

\int_{5}^{10} \frac{2}{( x + 2 ) ^{2}} d x

Take the constant out:

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

= 2 \cdot \int_{5}^{10} \frac{1}{( x + 2 ) ^{2}} d x

Apply u-substitution

: \int_{7}^{12} \frac{1}{u ^{2}} d u

= 2 \cdot \int_{7}^{12} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{7}^{12}

= 2 [- \frac{1}{u}]_{7}^{12}

Compute the boundaries:

\frac{5}{84}

= 2 \cdot \frac{5}{84}

Simplify

= \frac{5}{42}

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What is the integral from 5 to 10 of 2/((x+2)^2) ?
The integral from 5 to 10 of 2/((x+2)^2) is 5/42