What is the integral of 2ysin(x)+2 ?

The integral of 2ysin(x)+2 is 2y+y^2sin(x)+C

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integral of 2ysin(x)+2

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

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

Solution steps

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

\int 2 d y = 2 y

\int 2 sin (x) y d y = y^{2} sin (x)

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

Add a constant to the solution

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

f (x) = x^{x}

x \to 0 lim (\frac{( 1 - x ) ^{n} - 1}{x})

\int \frac{x - 2}{x - 1} d x

\int x^{3} e^{\frac{x}{2}} d x

\frac{d}{d x} ((3 x^{2} + 7)^{3})

What is the integral of 2ysin(x)+2 ?
The integral of 2ysin(x)+2 is 2y+y^2sin(x)+C