What is the integral of ((x+3))/((x+4)) ?

The integral of ((x+3))/((x+4)) is -ln|x+4|+x+C

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integral of ((x+3))/((x+4))

\int \frac{( x + 3 )}{( x + 4 )} d x

- ln ∣ x + 4 ∣ + x + C

Solution steps

\int \frac{x + 3}{x + 4} d x

\frac{x + 3}{x + 4} = - \frac{1}{x + 4} + 1

= \int - \frac{1}{x + 4} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{1}{x + 4} d x + \int 1 d x

\int \frac{1}{x + 4} d x = ln ∣ x + 4 ∣

\int 1 d x = x

= - ln ∣ x + 4 ∣ + x

Add a constant to the solution

= - ln ∣ x + 4 ∣ + x + C

\frac{d}{d x} (4 x^{3} + 3 x^{2} + 2 x + 1)

y = 2 x^{2} - 5

n = 1 \sum \infty 5^{\frac{1}{n}}

\int tan^{9} (x) sec^{2} (x) d x

\int_{2}^{6} \frac{x - 4}{x + 1} d x

What is the integral of ((x+3))/((x+4)) ?
The integral of ((x+3))/((x+4)) is -ln|x+4|+x+C