What is the integral of 2xy^2+3x^2 ?

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

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integral of 2xy^2+3x^2

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (y^{2} sin (\frac{x}{y}))

y = x^{3}, y = x^{2} - 2 x, [- 1, 1]

\frac{2}{3} x^{3} + x^{2} - 12 x + 12

f (t) = t

y^{^{'}} = e^{5 x + 4 y}