What is the integral of ycos(x)+2xe^y ?

The integral of ycos(x)+2xe^y is ysin(x)+e^yx^2+C

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integral of ycos(x)+2xe^y

\int y cos (x) + 2 x e^{y} d x

y sin (x) + e^{y} x^{2} + C

Solution steps

\int y cos (x) + 2 x e^{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 cos (x) y d x + \int 2 e^{y} x d x

\int cos (x) y d x = y sin (x)

\int 2 e^{y} x d x = e^{y} x^{2}

= y sin (x) + e^{y} x^{2}

Add a constant to the solution

= y sin (x) + e^{y} x^{2} + C

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What is the integral of ycos(x)+2xe^y ?
The integral of ycos(x)+2xe^y is ysin(x)+e^yx^2+C