Integral of (x^2+3x*y)*d*y dx
The solution
Detail solution
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The integral of a constant times a function is the constant times the integral of the function:
∫dy(x2+3xy)dx=dy∫(x2+3xy)dx
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Integrate term-by-term:
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The integral of xn is n+1xn+1 when n=−1:
∫x2dx=3x3
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The integral of a constant times a function is the constant times the integral of the function:
∫3xydx=3y∫xdx
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The integral of xn is n+1xn+1 when n=−1:
∫xdx=2x2
So, the result is: 23x2y
The result is: 3x3+23x2y
So, the result is: dy(3x3+23x2y)
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Now simplify:
6dx2y(2x+9y)
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Add the constant of integration:
6dx2y(2x+9y)+constant
The answer is:
6dx2y(2x+9y)+constant
The answer (Indefinite)
[src]
/
| / 3 2\
| / 2 \ |x 3*y*x |
| \x + 3*x*y/*d*y dx = C + d*y*|-- + ------|
| \3 2 /
/
dy(23x2y+3x3)
3 2 4 2
3*d *y y*d d*y 3*d*y
- ------- - ---- + --- + ------
2 3 3 2
dy(69y+2−69d2y+2d3)
=
3 2 4 2
3*d *y y*d d*y 3*d*y
- ------- - ---- + --- + ------
2 3 3 2
−3d4y−23d3y2+23dy2+3dy
Use the examples entering the upper and lower limits of integration.