What is the integral of 1+e^xsin(y) ?

The integral of 1+e^xsin(y) is x+sin(y)e^x+C

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integral of 1+e^xsin(y)

\int 1 + e^{x} sin (y) d x

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

Solution steps

\int 1 + 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 1 d x + \int sin (y) e^{x} d x

\int 1 d x = x

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

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

Add a constant to the solution

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

\frac{d y}{d x} = \frac{( x + 3 y )}{( y - 3 x )}

y^{^{'}} = 3 x

\frac{d}{d x} (e^{- 2 \cdot x})

x^{3} + e^{x}

\int 9 + t^{2} d t

What is the integral of 1+e^xsin(y) ?
The integral of 1+e^xsin(y) is x+sin(y)e^x+C