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

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

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integral of (y*e^x+sin(y))

\int (y \cdot 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}^{π} 6 cos^{4} (x) sin (x) d x

x \to - 0.1 lim (1 + e^{x})

4 y - y^{^{''}} = 10 e^{(- 3 x)}

e^{2 x + y} y^{^{'}} = e^{x - y}

\frac{d}{d x} (x^{5} - 5 x^{3})

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