What is the integral of 1+y^2+xy^2 ?

The integral of 1+y^2+xy^2 is x+y^2x+(y^2x^2)/2+C

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integral of 1+y^2+xy^2

\int 1 + y^{2} + x y^{2} d x

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

Solution steps

\int 1 + y^{2} + 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 1 d x + \int y^{2} d x + \int y^{2} x d x

\int 1 d x = x

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

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

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

Add a constant to the solution

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

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What is the integral of 1+y^2+xy^2 ?
The integral of 1+y^2+xy^2 is x+y^2x+(y^2x^2)/2+C