What is the integral of 8x^6y^3+15x^5y^4 ?

The integral of 8x^6y^3+15x^5y^4 is 3x^5y^5+2x^6y^4+C

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integral of 8x^6y^3+15x^5y^4

\int 8 x^{6} y^{3} + 15 x^{5} y^{4} d y

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

Solution steps

\int 8 x^{6} y^{3} + 15 x^{5} y^{4} 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 15 x^{5} y^{4} d y + \int 8 x^{6} y^{3} d y

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

\int 8 x^{6} y^{3} d y = 2 x^{6} y^{4}

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

Add a constant to the solution

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

What is the integral of 8x^6y^3+15x^5y^4 ?
The integral of 8x^6y^3+15x^5y^4 is 3x^5y^5+2x^6y^4+C