What is the integral of (2x+4)/(x^2+4x+13) ?

The integral of (2x+4)/(x^2+4x+13) is ln|x^2+4x+13|+C

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integral of (2x+4)/(x^2+4x+13)

\int \frac{2 x + 4}{x ^{2} + 4 x + 13} d x

ln x^{2} + 4 x + 13 + C

Solution steps

\int \frac{2 x + 4}{x ^{2} + 4 x + 13} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{2} + 4 x + 13

= ln x^{2} + 4 x + 13

Add a constant to the solution

= ln x^{2} + 4 x + 13 + C

n = 0 \sum \infty 1400700

n = 1 \sum \infty (\frac{5}{n})^{4}

y = e^{2 x} cos (π x), (0, 1)

f (x) = \frac{x + 7}{8 x}

\frac{d}{d x} (\frac{1}{sin ^{3} ( x )})

What is the integral of (2x+4)/(x^2+4x+13) ?
The integral of (2x+4)/(x^2+4x+13) is ln|x^2+4x+13|+C