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

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

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integral of 2xy^3+y^6

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

y^{6} x + y^{3} x^{2} + C

Solution steps

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

\int y^{6} d x = y^{6} x

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

= y^{6} x + y^{3} x^{2}

Add a constant to the solution

= y^{6} x + y^{3} x^{2} + C

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