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

- x y + (3 + x) (\frac{d y}{d x}) = 0

\int_{0}^{\frac{1}{2}} 2 arccos (x) d x

\int \frac{20}{x ^{- 1} + 5} d x

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

n = 1 \sum \infty 8 (0.8)^{n - 1}

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