What is the integral of ye^x+sin(y) ?

The integral of ye^x+sin(y) is sin(y)x+ye^x+C

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integral of ye^x+sin(y)

\int y e^{x} + sin (y) d x

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

Solution steps

\int y e^{x} + sin (y) 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 sin (y) d x + \int y e^{x} d x

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

\int y e^{x} d x = y e^{x}

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

Add a constant to the solution

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

\int_{0}^{2} 2 x^{2} x^{3} + 1 d x

y^{^{''}} + 16 y = 24 sec (4 t)

x \to - 4 + lim (f (x))

x^{2} + x y + 2 y^{2} = 32, (5, 1)

What is the integral of ye^x+sin(y) ?
The integral of ye^x+sin(y) is sin(y)x+ye^x+C