What is the integral of (4y+2x-5) ?

The integral of (4y+2x-5) is -5x+x^2+4yx+C

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integral of (4y+2x-5)

\int (4 y + 2 x - 5) d x

- 5 x + x^{2} + 4 y x + C

Solution steps

\int 4 y + 2 x - 5 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 5 d x + \int 2 x d x + \int 4 y d x

\int 5 d x = 5 x

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

\int 4 y d x = 4 y x

= - 5 x + x^{2} + 4 y x

Add a constant to the solution

= - 5 x + x^{2} + 4 y x + C

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