What is the integral of (12x^2e^{-4xy}-5x+1) ?

The integral of (12x^2e^{-4xy}-5x+1) is y-5xy-3xe^{-4xy}+C

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integral of (12x^2e^{-4xy}-5x+1)

\int (12 x^{2} e^{- 4 x y} - 5 x + 1) d y

y - 5 x y - 3 x e^{- 4 x y} + C

Solution steps

\int 12 x^{2} e^{- 4 x y} - 5 x + 1 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 1 d y - \int 5 x d y + \int 12 x^{2} e^{- 4 x y} d y

\int 1 d y = y

\int 5 x d y = 5 x y

\int 12 x^{2} e^{- 4 x y} d y = - 3 x e^{- 4 x y}

= y - 5 x y - 3 x e^{- 4 x y}

Add a constant to the solution

= y - 5 x y - 3 x e^{- 4 x y} + C

What is the integral of (12x^2e^{-4xy}-5x+1) ?
The integral of (12x^2e^{-4xy}-5x+1) is y-5xy-3xe^{-4xy}+C