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

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

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integral of y^2cos(x)-sin(x)

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

- 5, 2, 2 x^{2} + 3, 0

x \to 0 lim (\frac{1 2 ^{x} - 5 ^{x}}{x})

\frac{d}{d x} (\frac{2 x}{4 x ^{2} + 4})

\int 20 x^{2} + 3 x - 9 d x

\int (6 x^{3} + 3 x^{2}) d x

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