What is the integral of 50-(100)/(x+25) ?

The integral of 50-(100)/(x+25) is 50x-100ln|x+25|+C

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integral of 50-(100)/(x+25)

\int 50 - \frac{100}{x + 25} d x

50 x - 100 ln ∣ x + 25 ∣ + C

Solution steps

\int 50 - \frac{100}{x + 25} 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 50 d x - \int \frac{100}{x + 25} d x

\int 50 d x = 50 x

\int \frac{100}{x + 25} d x = 100 ln ∣ x + 25 ∣

= 50 x - 100 ln ∣ x + 25 ∣

Add a constant to the solution

= 50 x - 100 ln ∣ x + 25 ∣ + C

x \to - 1 lim (e^{\frac{1}{x + 1}})

y^{^{''}} - 5 y^{^{'}} = (5 t + 9) sin (2 t)

4 x - 2

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

\int (x^{3} + 10 x - 3) d x

What is the integral of 50-(100)/(x+25) ?
The integral of 50-(100)/(x+25) is 50x-100ln|x+25|+C