What is the integral of (ln(y)+2xy^3) ?

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

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integral of (ln(y)+2xy^3)

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

ln (y) x + y^{3} x^{2} + C

Solution steps

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

\int ln (y) d x = ln (y) x

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

= ln (y) x + y^{3} x^{2}

Add a constant to the solution

= ln (y) x + y^{3} x^{2} + C

What is the integral of (ln(y)+2xy^3) ?
The integral of (ln(y)+2xy^3) is ln(y)x+y^3x^2+C