What is the integral of ln(y)+4xy^3 ?

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

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integral of ln(y)+4xy^3

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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

\frac{s + 3}{s ^{2} + 4 s + 5}

\int \frac{11}{2 x 4 x ^{2} - 16} d x

\int \frac{( a x + b )}{( c x + d )} d x

\frac{7}{2 x ^{2}}

What is the integral of ln(y)+4xy^3 ?
The integral of ln(y)+4xy^3 is ln(y)x+2y^3x^2+C