What is the integral of (4cos(x+4y)+ze^{yz}) ?

The integral of (4cos(x+4y)+ze^{yz}) is sin(x+4y)+e^{zy}+C

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integral of (4cos(x+4y)+ze^{yz})

\int (4 cos (x + 4 y) + z e^{yz}) d y

sin (x + 4 y) + e^{zy} + C

Solution steps

\int 4 cos (x + 4 y) + z e^{yz} 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 4 cos (x + 4 y) d y + \int z e^{zy} d y

\int 4 cos (x + 4 y) d y = sin (x + 4 y)

\int z e^{zy} d y = e^{zy}

= sin (x + 4 y) + e^{zy}

Add a constant to the solution

= sin (x + 4 y) + e^{zy} + C

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What is the integral of (4cos(x+4y)+ze^{yz}) ?
The integral of (4cos(x+4y)+ze^{yz}) is sin(x+4y)+e^{zy}+C