What is the integral of (2x+ycos(xy)) ?

The integral of (2x+ycos(xy)) is x^2+sin(yx)+C

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integral of (2x+ycos(xy))

\int (2 x + y cos (x y)) d x

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

Solution steps

\int 2 x + y cos (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 2 x d x + \int cos (y x) y d x

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

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

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

Add a constant to the solution

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

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

\int \frac{sin ( x ) cos ( x )}{2 + sin ^{2} ( x )} d x

\int z z - 8 d z

3 x

\int \frac{x ^{2}}{( 4 - x ^{2} ) ^{3}} d x

What is the integral of (2x+ycos(xy)) ?
The integral of (2x+ycos(xy)) is x^2+sin(yx)+C