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

The integral of ((2x+4))/(x^2+4x+5) is ln|x^2+4x+5|+C

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integral of ((2x+4))/(x^2+4x+5)

\int \frac{( 2 x + 4 )}{x ^{2} + 4 x + 5} d x

ln x^{2} + 4 x + 5 + C

Solution steps

\int \frac{2 x + 4}{x ^{2} + 4 x + 5} 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 + 5

= ln x^{2} + 4 x + 5

Add a constant to the solution

= ln x^{2} + 4 x + 5 + C

\int \frac{x ^{2} + 2 x + 3}{x ^{3} + 3 x ^{2} + 9 x + 1} d x

\int \frac{1}{2 x ^{2} + x} d x

sin (x), - sin (x), [0, 4]

\int \frac{10 x ^{3} - 5 x ^{2} + 4 x}{x ^{2}} d x

\frac{d}{d x} (tanh (2 x - 3))

What is the integral of ((2x+4))/(x^2+4x+5) ?
The integral of ((2x+4))/(x^2+4x+5) is ln|x^2+4x+5|+C