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

\int x^{\frac{1}{2}} + 7 d x

\int y (y + 1)^{2} d y

\int \frac{- x ^{2}}{x ^{2} + x - 2} d x

\int \frac{x + 4}{x ^{3} - 2 x ^{2} + x} d x

\int (x^{8} + \frac{1}{x ^{8}}) d x

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