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

y = x^{3} - 4 x, (- 2, 0)

\int_{1}^{e^{2}} \frac{ln ^{8} ( x ^{2} )}{x} d x

5 e^{x}

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

y = 3 x^{2} + 3, (2, 15)

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