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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

f (x) = x^{2} \cdot e^{x^{2} - 1}, at x = - 1

\int (x - 1) x^{2} - 2 x d x

\frac{d}{d h} (35 f (h) (3 + 2 h))

(1 + \frac{x}{2})^{- 4}

\int 16 - x d x

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