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

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

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integral of 3x^2-2y^2

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

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

Solution steps

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

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

\int 3 x^{2} d x = x^{3}

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

Add a constant to the solution

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

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

x \to 1 lim (3 + f (x))

\int t^{2} e^{- 4 t} d t

\frac{d}{d x} (\frac{4 x}{7 x - 2})

\frac{1}{( 2 s + 1 ) s}