What is the integral of 4x^3+2xy^2 ?

The integral of 4x^3+2xy^2 is x^4+y^2x^2+C

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integral of 4x^3+2xy^2

\int 4 x^{3} + 2 x y^{2} d x

x^{4} + y^{2} x^{2} + C

Solution steps

\int 4 x^{3} + 2 x 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 4 x^{3} d x + \int 2 y^{2} x d x

\int 4 x^{3} d x = x^{4}

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

= x^{4} + y^{2} x^{2}

Add a constant to the solution

= x^{4} + y^{2} x^{2} + C

\frac{\partial}{\partial x} (x^{\frac{1}{2}} y^{\frac{1}{3}})

4^{x}

\int_{0}^{4} x e^{- 3 x} d x

\int (x - \frac{1}{2} x + \frac{2}{x}) d x

x^{- \frac{3}{5}} + x^{\frac{3}{5}}