What is the integral of y+y^2cos(x) ?

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

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integral of y+y^2cos(x)

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

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

Solution steps

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

\int y d x = y x

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

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

Add a constant to the solution

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

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