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

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

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integral of (e^xsin(y)-y)

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

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

Solution steps

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

\int y d x = y x

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

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

Add a constant to the solution

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

ln (tan^{2} (x))

y = x, y = x^{2} - 2, y = 0

x y^{^{'}} - 2 y = x^{4}

n = 0 \sum \infty e^{(2 n - 1)}

\int \frac{2 x + 1}{x ^{2} - x + 3} d x

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