What is the integral from-2 to 1 of 1/((11+5x)^2) ?

The integral from-2 to 1 of 1/((11+5x)^2) is 3/16

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integral from-2 to 1 of 1/((11+5x)^2)

\int_{- 2}^{1} \frac{1}{( 11 + 5 x ) ^{2}} d x

\frac{3}{16}

Decimal

0.1875

Solution steps

\int_{- 2}^{1} \frac{1}{( 11 + 5 x ) ^{2}} d x

Apply u-substitution

: \int_{1}^{16} \frac{1}{5 u ^{2}} d u

= \int_{1}^{16} \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_{1}^{16} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{1}^{16}

= \frac{1}{5} [- \frac{1}{u}]_{1}^{16}

Compute the boundaries:

\frac{15}{16}

= \frac{1}{5} \cdot \frac{15}{16}

Simplify

= \frac{3}{16}

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What is the integral from-2 to 1 of 1/((11+5x)^2) ?
The integral from-2 to 1 of 1/((11+5x)^2) is 3/16