What is the integral of 2xe^{2y}-xcos(xy)+2y ?

The integral of 2xe^{2y}-xcos(xy)+2y is y^2-sin(xy)+xe^{2y}+C

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integral of 2xe^{2y}-xcos(xy)+2y

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

y^{2} - sin (x y) + x e^{2 y} + C

Solution steps

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

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

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

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

= y^{2} - sin (x y) + x e^{2 y}

Add a constant to the solution

= y^{2} - sin (x y) + x e^{2 y} + C

\int - \frac{1}{1 + e ^{- x}} d x

\int (\frac{x}{1 - 4 x ^{2}}) d x

\int \frac{( 2 x + 1 )}{x ^{2} - 9} d x

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

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

What is the integral of 2xe^{2y}-xcos(xy)+2y ?
The integral of 2xe^{2y}-xcos(xy)+2y is y^2-sin(xy)+xe^{2y}+C