What is the integral of (x^3+y^3) ?

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

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integral of (x^3+y^3)

\int (x^{3} + y^{3}) d x

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

Solution steps

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

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

Add a constant to the solution

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

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