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

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

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integral of sin(y)+ye^x

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

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

Solution steps

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

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\int sin (5 x) cos^{3} (5 x) d x

\int \frac{e ^{2 x} + 4}{e ^{2 x} + e ^{- 2 x}} d x

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