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

5 x - 4

\int \frac{y}{y + 6} d y

\int 2 x (x^{2} - 1)^{2} d x

x = 20 - 5 y^{2}, x = 5 y^{2} - 20

x \to 3 lim (\frac{3}{9 - x ^{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