What is the integral of 2xy-sin(x) ?

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

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integral of 2xy-sin(x)

\int 2 x y - sin (x) d x

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

Solution steps

\int 2 x y - sin (x) 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 sin (x) d x + \int 2 y x d x

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

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

= - (- cos (x)) + y x^{2}

Simplify

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

Add a constant to the solution

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

f (x) = (x + 1) (3 x^{2} - 5 x + 2)

y^{^{''}} - y^{^{'}} - y = 0

x \to 4 lim (2 x - 1)

\frac{d}{d x} (2 e^{x} ln (x))

x \to - 2 lim (- x^{2} + 8 x - 4)

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