What is the integral of (xy^2+x^2+y+4) ?

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

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integral of (xy^2+x^2+y+4)

\int (x y^{2} + x^{2} + y + 4) d x

4 x + y x + \frac{x ^{3}}{3} + \frac{y ^{2} x ^{2}}{2} + C

Solution steps

\int x y^{2} + x^{2} + y + 4 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 4 d x + \int y d x + \int x^{2} d x + \int y^{2} x d x

\int 4 d x = 4 x

\int y d x = y x

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

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

= 4 x + y x + \frac{x ^{3}}{3} + \frac{y ^{2} x ^{2}}{2}

Add a constant to the solution

= 4 x + y x + \frac{x ^{3}}{3} + \frac{y ^{2} x ^{2}}{2} + C

(\frac{x}{x ^{5} + 1})^{^{'}}

f (v) = (v^{- 3} + 3 v^{- 2})^{3}

f^{^{'}} (x) = 7 x^{4}

x \to - 3 lim (x^{2} + 7 x - 6)

x \to 9 + lim (\frac{6}{x - 9})

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