What is the integral of (sin(7x)-cos(2y)+(5x)/(y+4)) ?

The integral of (sin(7x)-cos(2y)+(5x)/(y+4)) is -1/2 sin(2y)+5xln|4+y|+sin(7x)y+C

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integral of (sin(7x)-cos(2y)+(5x)/(y+4))

\int (sin (7 x) - cos (2 y) + \frac{5 x}{y + 4}) d y

- \frac{1}{2} sin (2 y) + 5 x ln ∣ 4 + y ∣ + sin (7 x) y + C

Solution steps

\int sin (7 x) - cos (2 y) + \frac{5 x}{y + 4} 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 cos (2 y) d y + \int \frac{5 x}{4 + y} d y + \int sin (7 x) d y

\int cos (2 y) d y = \frac{1}{2} sin (2 y)

\int \frac{5 x}{4 + y} d y = 5 x ln ∣ 4 + y ∣

\int sin (7 x) d y = sin (7 x) y

= - \frac{1}{2} sin (2 y) + 5 x ln ∣ 4 + y ∣ + sin (7 x) y

Add a constant to the solution

= - \frac{1}{2} sin (2 y) + 5 x ln ∣ 4 + y ∣ + sin (7 x) y + C

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What is the integral of (sin(7x)-cos(2y)+(5x)/(y+4)) ?
The integral of (sin(7x)-cos(2y)+(5x)/(y+4)) is -1/2 sin(2y)+5xln|4+y|+sin(7x)y+C