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

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

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

\int_{1}^{5} \frac{4}{x ^{2} + 2 x + 1} d x

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

\int_{1}^{5} \frac{4}{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

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

Complete the square

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

= 4 \cdot \int_{1}^{5} \frac{1}{( x + 1 ) ^{2}} d x

Apply u-substitution

: \int_{2}^{6} \frac{1}{u ^{2}} d u

= 4 \cdot \int_{2}^{6} \frac{1}{u ^{2}} d u

Apply the Power Rule

: [- \frac{1}{u}]_{2}^{6}

= 4 [- \frac{1}{u}]_{2}^{6}

Compute the boundaries:

\frac{1}{3}

= 4 \cdot \frac{1}{3}

Simplify

= \frac{4}{3}

\int \frac{sin ( x )}{cos ^{3} ( x )} d x

\frac{d}{d x} (- \frac{1}{( 1 - x ) ^{2}})

y = arctan (4 t)

x \to 2 + lim (\frac{4 x}{x - 2})

x y^{^{'}} - 2 y = x^{2} - 2 x - 1

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