Integral of y(x^2+y^2) 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:
∫y(x2+y2)dx=y∫(x2+y2)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 is the constant times the variable of integration:
∫y2dx=xy2
The result is: 3x3+xy2
So, the result is: y(3x3+xy2)
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Now simplify:
xy(3x2+y2)
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Add the constant of integration:
xy(3x2+y2)+constant
The answer is:
xy(3x2+y2)+constant
The answer (Indefinite)
[src]
/
| / 3 \
| / 2 2\ |x 2|
| y*\x + y / dx = C + y*|-- + x*y |
| \3 /
/
∫y(x2+y2)dx=C+y(3x3+xy2)
y3+3y
=
y3+3y
Use the examples entering the upper and lower limits of integration.