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

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

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integral of (e^xsin(y)+tan(y))

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (y ln (y) + y e^{x})

\frac{d}{d l} (\frac{d l ^{2} - d - a l ^{3} - b l ^{2}}{l ^{2}})

\int \frac{sin ( 2 x )}{( 1 - cos ^{2} ( x ) ) ^{3}} d x

\frac{- 3}{( s + 3 ) ^{2}}

17 e^{x}

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