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

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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

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

Apply the Power Rule

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

Compute the boundaries:

\frac{1}{4}

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

Simplify

= \frac{5}{4}

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