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

The integral from 1 to 3 of 5/(x^2+2x+1) is 5/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int_{1}^{3} \frac{5}{x ^{2} + 2 x + 1} d x

\frac{5}{4}

Decimal

1.25

Solution steps

\int_{1}^{3} \frac{5}{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

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

Complete the square

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

= 5 \cdot \int_{1}^{3} \frac{1}{( x + 1 ) ^{2}} d x

Apply u-substitution

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

= 5 \cdot \int_{2}^{4} \frac{1}{u ^{2}} d u

Apply the Power Rule

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

= 5 [- \frac{1}{u}]_{2}^{4}

Compute the boundaries:

\frac{1}{4}

= 5 \cdot \frac{1}{4}

Simplify

= \frac{5}{4}

f (x) = ln (5 - x)

\frac{d}{d x} (ln (x + y + 5))

\int \frac{1}{200 - x} d x

\frac{d y}{d t} + e^{t} y = - 18 e^{t}

\frac{d}{d x} (4 + 4 x)

What is the integral from 1 to 3 of 5/(x^2+2x+1) ?
The integral from 1 to 3 of 5/(x^2+2x+1) is 5/4