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

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

Popular >

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Complete the square

x^{2} + 2 x + 1 : (x + 1)^{2}

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

Apply u-substitution

: \int_{2}^{4} \frac{1}{u ^{2}} d u

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{4}

= 2 \cdot \frac{1}{4}

Simplify

= \frac{1}{2}

f (x) = x^{2} + 5, at x = - 2

\frac{16}{4 + x ^{2}}, y = 1

y = \frac{1}{4 - 9 x ^{2}}, (0, \frac{1}{3})

\frac{d}{d x} (- 7 sin (cos (x)))

\frac{\partial}{\partial x} (\frac{4 x - 4 z}{y + 4 z})

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