What is the integral of 3x^2y^2+x/y ?

The integral of 3x^2y^2+x/y is xln|y|+x^2y^3+C

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integral of 3x^2y^2+x/y

\int 3 x^{2} y^{2} + \frac{x}{y} d y

x ln ∣ y ∣ + x^{2} y^{3} + C

Solution steps

\int 3 x^{2} y^{2} + \frac{x}{y} d y

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{x}{y} d y + \int 3 x^{2} y^{2} d y

\int \frac{x}{y} d y = x ln ∣ y ∣

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

= x ln ∣ y ∣ + x^{2} y^{3}

Add a constant to the solution

= x ln ∣ y ∣ + x^{2} y^{3} + C

What is the integral of 3x^2y^2+x/y ?
The integral of 3x^2y^2+x/y is xln|y|+x^2y^3+C