What is the integral of 2/(x+5)-cos(3x) ?

The integral of 2/(x+5)-cos(3x) is 2ln|x+5|-1/3 sin(3x)+C

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integral of 2/(x+5)-cos(3x)

\int \frac{2}{x + 5} - cos (3 x) d x

2 ln ∣ x + 5 ∣ - \frac{1}{3} sin (3 x) + C

Solution steps

\int \frac{2}{x + 5} - cos (3 x) 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{2}{x + 5} d x - \int cos (3 x) d x

\int \frac{2}{x + 5} d x = 2 ln ∣ x + 5 ∣

\int cos (3 x) d x = \frac{1}{3} sin (3 x)

= 2 ln ∣ x + 5 ∣ - \frac{1}{3} sin (3 x)

Add a constant to the solution

= 2 ln ∣ x + 5 ∣ - \frac{1}{3} sin (3 x) + C

\frac{8 x - 6}{x - 6}

y^{^{'}} - 4 y = 0.8

(x - 1)^{2} (x - 2) (x - 4)

\int sinh (3 u) d u

\frac{d}{d x} ((- x)^{2})

What is the integral of 2/(x+5)-cos(3x) ?
The integral of 2/(x+5)-cos(3x) is 2ln|x+5|-1/3 sin(3x)+C