What is the integral of y^3+10xy^4-2x ?

The integral of y^3+10xy^4-2x is y^3x-x^2+5y^4x^2+C

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integral of y^3+10xy^4-2x

\int y^{3} + 10 x y^{4} - 2 x d x

y^{3} x - x^{2} + 5 y^{4} x^{2} + C

Solution steps

\int y^{3} + 10 x y^{4} - 2 x 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^{3} d x - \int 2 x d x + \int 10 y^{4} x d x

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

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

\int 10 y^{4} x d x = 5 y^{4} x^{2}

= y^{3} x - x^{2} + 5 y^{4} x^{2}

Add a constant to the solution

= y^{3} x - x^{2} + 5 y^{4} x^{2} + C

x \to - 4 - lim (\frac{x + 3}{x + 4})

f (x) = x 8 - x^{2}

\frac{d}{d x} (\frac{x + 2}{x + 3})

\int 0.02

\int \frac{sin ( x )}{7 - cos ^{2} ( x )} d x

What is the integral of y^3+10xy^4-2x ?
The integral of y^3+10xy^4-2x is y^3x-x^2+5y^4x^2+C