What is the integral of 5/y+sin(y) ?

The integral of 5/y+sin(y) is 5ln|y|-cos(y)+C

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integral of 5/y+sin(y)

\int \frac{5}{y} + sin (y) d y

5 ln ∣ y ∣ - cos (y) + C

Solution steps

\int \frac{5}{y} + sin (y) d y

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{5}{y} d y + \int sin (y) d y

\int \frac{5}{y} d y = 5 ln ∣ y ∣

\int sin (y) d y = - cos (y)

= 5 ln ∣ y ∣ - cos (y)

Add a constant to the solution

= 5 ln ∣ y ∣ - cos (y) + C

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\int \frac{1}{1 - e ^{- 3 x}} d x

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What is the integral of 5/y+sin(y) ?
The integral of 5/y+sin(y) is 5ln|y|-cos(y)+C