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

The integral of (2xy+4x^3) is x^4+yx^2+C

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integral of (2xy+4x^3)

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

x \to 0 + lim (\frac{ln ( x )}{x})

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