Math  /  Calculus

Questione3x(3yx2+2xy+y3)dx+e3x(x2+y2)dy\int e^{3 x}\left(3 y x^{2}+2 x y+y^{3}\right) d x+\int e^{3 x}\left(x^{2}+y^{2}\right) d y

Studdy Solution
Combine the results from both integrals:
The final result is:
yx2e3x+13y3e3x+e3xx2y+e3xy33 yx^2e^{3x} + \frac{1}{3}y^3e^{3x} + e^{3x}x^2 y + e^{3x} \cdot \frac{y^3}{3}
Simplify if possible:
2yx2e3x+23y3e3x 2yx^2e^{3x} + \frac{2}{3}y^3e^{3x}
The solution to the problem is:
2yx2e3x+23y3e3x 2yx^2e^{3x} + \frac{2}{3}y^3e^{3x}

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