What is the integral from 1 to 3 of 2/(x^2+4x+4) ?

The integral from 1 to 3 of 2/(x^2+4x+4) is 4/15

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integral from 1 to 3 of 2/(x^2+4x+4)

\int_{1}^{3} \frac{2}{x ^{2} + 4 x + 4} d x

\frac{4}{15}

Decimal Notation

0.26666 \dots

Solution steps

\int_{1}^{3} \frac{2}{x ^{2} + 4 x + 4} d x

Take the constant out:

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

= 2 \cdot \int_{1}^{3} \frac{1}{x ^{2} + 4 x + 4} d x

Complete the square

x^{2} + 4 x + 4 : (x + 2)^{2}

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

Apply u-substitution

: \int_{3}^{5} \frac{1}{u ^{2}} d u

= 2 \cdot \int_{3}^{5} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{3}^{5}

= 2 [- \frac{1}{u}]_{3}^{5}

Compute the boundaries:

\frac{2}{15}

= 2 \cdot \frac{2}{15}

Simplify

= \frac{4}{15}

\frac{d}{d x} ((sec (x)) d x)

\int \frac{1}{x ^{2} + 6 x + 15} d x

y = \frac{1}{2} x + \frac{1}{4} x sin (2 x)

f (x) = x x, at x = 4

\int \frac{( e ^{x} )}{e ^{x} ( e ^{x} - 3 )} d x

What is the integral from 1 to 3 of 2/(x^2+4x+4) ?
The integral from 1 to 3 of 2/(x^2+4x+4) is 4/15