What is the integral of 12x^5y^4+15x^4y^5 ?

The integral of 12x^5y^4+15x^4y^5 is 2y^4x^6+3y^5x^5+C

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integral of 12x^5y^4+15x^4y^5

\int 12 x^{5} y^{4} + 15 x^{4} y^{5}

2 y^{4} x^{6} + 3 y^{5} x^{5} + C

Solution steps

\int 12 x^{5} y^{4} + 15 x^{4} y^{5} 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 12 y^{4} x^{5} d x + \int 15 y^{5} x^{4} d x

\int 12 y^{4} x^{5} d x = 2 y^{4} x^{6}

\int 15 y^{5} x^{4} d x = 3 y^{5} x^{5}

= 2 y^{4} x^{6} + 3 y^{5} x^{5}

Add a constant to the solution

= 2 y^{4} x^{6} + 3 y^{5} x^{5} + C

What is the integral of 12x^5y^4+15x^4y^5 ?
The integral of 12x^5y^4+15x^4y^5 is 2y^4x^6+3y^5x^5+C