What is the integral of y^2e^{xy}+cos(x) ?

The integral of y^2e^{xy}+cos(x) is sin(x)+ye^{yx}+C

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integral of y^2e^{xy}+cos(x)

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (1 - y^{3})

\frac{d y}{d x} = \frac{1 + x}{y}

x \to 0 lim (\frac{7}{x ^{2} + x} - \frac{7}{x})

\frac{\partial}{\partial x} (\frac{x y}{x + 1})

\frac{( s + 2 )}{( s + 1 ) ^{2}}

What is the integral of y^2e^{xy}+cos(x) ?
The integral of y^2e^{xy}+cos(x) is sin(x)+ye^{yx}+C