What is the integral of (xcos(y)+5xe^{5xy}) ?

The integral of (xcos(y)+5xe^{5xy}) is xsin(y)+e^{5xy}+C

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integral of (xcos(y)+5xe^{5xy})

\int (x cos (y) + 5 x e^{5 x y}) d y

x sin (y) + e^{5 x y} + C

Solution steps

\int x cos (y) + 5 x e^{5 x y} d y

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 (y) x d y + \int 5 x e^{5 x y} d y

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

\int 5 x e^{5 x y} d y = e^{5 x y}

= x sin (y) + e^{5 x y}

Add a constant to the solution

= x sin (y) + e^{5 x y} + C

What is the integral of (xcos(y)+5xe^{5xy}) ?
The integral of (xcos(y)+5xe^{5xy}) is xsin(y)+e^{5xy}+C