What is the integral of (10+2x^2+2y^2) ?

The integral of (10+2x^2+2y^2) is 10x+2y^2x+(2x^3)/3+C

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integral of (10+2x^2+2y^2)

\int (10 + 2 x^{2} + 2 y^{2}) d x

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

Solution steps

\int 10 + 2 x^{2} + 2 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 10 d x + \int 2 y^{2} d x + \int 2 x^{2} d x

\int 10 d x = 10 x

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

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

= 10 x + 2 y^{2} x + \frac{2 x ^{3}}{3}

Add a constant to the solution

= 10 x + 2 y^{2} x + \frac{2 x ^{3}}{3} + C

What is the integral of (10+2x^2+2y^2) ?
The integral of (10+2x^2+2y^2) is 10x+2y^2x+(2x^3)/3+C