What is the integral of 24xy^2+3ye^{xy} ?

The integral of 24xy^2+3ye^{xy} is 12y^2x^2+3e^{yx}+C

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integral of 24xy^2+3ye^{xy}

\int 24 x y^{2} + 3 y e^{x y} d x

12 y^{2} x^{2} + 3 e^{y x} + C

Solution steps

\int 24 x y^{2} + 3 y e^{x 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 24 y^{2} x d x + \int 3 y e^{y x} d x

\int 24 y^{2} x d x = 12 y^{2} x^{2}

\int 3 y e^{y x} d x = 3 e^{y x}

= 12 y^{2} x^{2} + 3 e^{y x}

Add a constant to the solution

= 12 y^{2} x^{2} + 3 e^{y x} + C

\frac{d y}{d x} = e^{(6 x - 3 y)}, y (0) = 3

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

f (x) = x^{2} (1 - 5 x)

\int \frac{30}{( 225 x ^{2} + 1 ) ^{2}} d x

\frac{10}{( 1 + e ^{- x} )}

What is the integral of 24xy^2+3ye^{xy} ?
The integral of 24xy^2+3ye^{xy} is 12y^2x^2+3e^{yx}+C