What is the integral from 0 to 4 of (x+1)/(x^2+2x+1) ?

The integral from 0 to 4 of (x+1)/(x^2+2x+1) is ln(5)

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integral from 0 to 4 of (x+1)/(x^2+2x+1)

\int_{0}^{4} \frac{x + 1}{x ^{2} + 2 x + 1} d x

ln (5)

Decimal Notation

1.60943 \dots

Solution steps

\int_{0}^{4} \frac{x + 1}{x ^{2} + 2 x + 1} d x

Apply u-substitution

: \int_{1}^{25} \frac{1}{2 u} d u

= \int_{1}^{25} \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{25} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{1}^{25}

Compute the boundaries:

2 ln (5)

= \frac{1}{2} \cdot 2 ln (5)

Simplify

= ln (5)

\int_{0}^{0.5} e^{- x^{3}} d x

\int_{- 3}^{4} ∣ x + 1 ∣ d x

\int_{1}^{6} (x^{3} + x^{2} + 3) d x

\int_{2}^{3} \frac{7}{x} + x^{- 1} d x

\int_{- 1}^{0} (2 x + 1)^{4} (x + 1) d x

What is the integral from 0 to 4 of (x+1)/(x^2+2x+1) ?
The integral from 0 to 4 of (x+1)/(x^2+2x+1) is ln(5)