What is the integral of 6y^2-x^2+3 ?

The integral of 6y^2-x^2+3 is 3y-x^2y+2y^3+C

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integral of 6y^2-x^2+3

\int 6 y^{2} - x^{2} + 3 d y

3 y - x^{2} y + 2 y^{3} + C

Solution steps

\int 6 y^{2} - x^{2} + 3 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 3 d y - \int x^{2} d y + \int 6 y^{2} d y

\int 3 d y = 3 y

\int x^{2} d y = x^{2} y

\int 6 y^{2} d y = 2 y^{3}

= 3 y - x^{2} y + 2 y^{3}

Add a constant to the solution

= 3 y - x^{2} y + 2 y^{3} + C

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What is the integral of 6y^2-x^2+3 ?
The integral of 6y^2-x^2+3 is 3y-x^2y+2y^3+C